universidad complutense de madrid - E

... - F. C OBOS , A. S EGURADO. Limiting real interpolation methods for arbitrary Banach couples. Studia Math. 213 (2012), 243–273. - F. C OBOS , A. S EGURADO. Bilinear operators and limiting real methods. In Function Spaces X. Vol. 102 of Banach Center Publ. (2014), 57–70. - F. C OBOS , A. S EGURADO. S ...

... - F. C OBOS , A. S EGURADO. Limiting real interpolation methods for arbitrary Banach couples. Studia Math. 213 (2012), 243–273. - F. C OBOS , A. S EGURADO. Bilinear operators and limiting real methods. In Function Spaces X. Vol. 102 of Banach Center Publ. (2014), 57–70. - F. C OBOS , A. S EGURADO. S ...

IOSR Journal of Mathematics (IOSR-JM)

... Continuity and its decomposition have been intensively studied in the eld of topology and other several branches of mathematics. Levine.N in [10] introduced the notion and decomposition of continuity in topological spaces. Jingcheng Tong in [6] in-troduced the notion of A-sets and A-continuity and e ...

... Continuity and its decomposition have been intensively studied in the eld of topology and other several branches of mathematics. Levine.N in [10] introduced the notion and decomposition of continuity in topological spaces. Jingcheng Tong in [6] in-troduced the notion of A-sets and A-continuity and e ...

D.K. Ray Chaudhuri; (1959)On the application of the geometry of quadrics to the construction of partially balanced incomplete block designs and error correcting binary codes."

... of sets in PG(n , s) • A series of two associate PBIB designs is obtained from the configuration of generators and points of a nondegenerate quadric taking generators for blocks and points for treatments. Three other series of two associate PBIB designs are obtained. series contain many designs with ...

... of sets in PG(n , s) • A series of two associate PBIB designs is obtained from the configuration of generators and points of a nondegenerate quadric taking generators for blocks and points for treatments. Three other series of two associate PBIB designs are obtained. series contain many designs with ...

Lesson

... WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain. Use the Distance Formula to show that the corresponding sides are congruent. ...

... WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain. Use the Distance Formula to show that the corresponding sides are congruent. ...

Stone duality above dimension zero

... The main object of study of this thesis is the dual of the category KHaus of compact Hausdorff spaces and continuous maps. A celebrated result by Stone [65] shows that the full subcategory St of the category KHaus, whose objects are Stone spaces (=zerodimensional compact Hausdorff spaces), is dually ...

... The main object of study of this thesis is the dual of the category KHaus of compact Hausdorff spaces and continuous maps. A celebrated result by Stone [65] shows that the full subcategory St of the category KHaus, whose objects are Stone spaces (=zerodimensional compact Hausdorff spaces), is dually ...

Representations of dynamical systems on Banach spaces

... systems and Banach spaces. A further indication for the success of this theory is the fact that it provides also a natural environment for the study of representations of topological groups and compact right topological semigroups on Banach spaces. Throughout our review there are some new results w ...

... systems and Banach spaces. A further indication for the success of this theory is the fact that it provides also a natural environment for the study of representations of topological groups and compact right topological semigroups on Banach spaces. Throughout our review there are some new results w ...

Conjugate conics and closed chains of Poncelet polygons

... (A1) Given any two distinct points, there is exactly one line incident with both of them. (A2) Given any two distinct lines, there is exactly one point incident with both of them. (A3) There are four points such that no line is incident with more than two of them. ...

... (A1) Given any two distinct points, there is exactly one line incident with both of them. (A2) Given any two distinct lines, there is exactly one point incident with both of them. (A3) There are four points such that no line is incident with more than two of them. ...

Haar Measure on LCH Groups

... Proposition 1.1. Let G be a topological group. Then: 1. Topology of G is translation invariant. i.e. U open =⇒ U x, xU open ∀x ∈ G. 2. For every neighborhood U of e, there is a symmetric neighborhood V of e such that V ⊂ U . 3. For every neighborhood U of e, there is a neighborhood V of e such that ...

... Proposition 1.1. Let G be a topological group. Then: 1. Topology of G is translation invariant. i.e. U open =⇒ U x, xU open ∀x ∈ G. 2. For every neighborhood U of e, there is a symmetric neighborhood V of e such that V ⊂ U . 3. For every neighborhood U of e, there is a neighborhood V of e such that ...

Non-archimedean analytic spaces

... Here are few basic examples of Banach rings. R and C are the only archimedean Banach fields. The only multiplicative norms on them are | |r∞ for 0 < r ≤ 1. Some non-archimedean valued fields are: fields k with the trivial valuation | |0 (i.e. |x|0 = 1 for x 6= 0), k (t) and k ((t)) with the t-adic n ...

... Here are few basic examples of Banach rings. R and C are the only archimedean Banach fields. The only multiplicative norms on them are | |r∞ for 0 < r ≤ 1. Some non-archimedean valued fields are: fields k with the trivial valuation | |0 (i.e. |x|0 = 1 for x 6= 0), k (t) and k ((t)) with the t-adic n ...

FunctionalDependencies2

... R is a relation schema and F is a set of FD’s over R. A binary decomposition of R into relation schemas R1 and R2 with attribute sets X and Y is said to be a lossless-join decomposition with respect to F, if for every instance r of R that satisfies F, we have X( r ) Y( r ) = r Thm: Let R be a r ...

... R is a relation schema and F is a set of FD’s over R. A binary decomposition of R into relation schemas R1 and R2 with attribute sets X and Y is said to be a lossless-join decomposition with respect to F, if for every instance r of R that satisfies F, we have X( r ) Y( r ) = r Thm: Let R be a r ...

Connectedness and local connectedness of topological groups and

... in the sense of Graev are connected iff X is connected. The situation in the case of the free (Abelian) topological group F (X) (resp., A(X)) is different: neither F (X) nor A(X) is connected for a non-empty space X. However, the groups F (X) and A(X) contain open normal subgroups F ∗ (X) and A∗ (X) ...

... in the sense of Graev are connected iff X is connected. The situation in the case of the free (Abelian) topological group F (X) (resp., A(X)) is different: neither F (X) nor A(X) is connected for a non-empty space X. However, the groups F (X) and A(X) contain open normal subgroups F ∗ (X) and A∗ (X) ...

A co-analytic Cohen indestructible maximal cofinitary group

... the continuum hypothesis. In this paper we answer these questions in the positive: Theorem 1.2. The existence of a Π11 mcg is consistent with arbitrarily large continuum (assuming the consistency of ZFC). At the same time, we give a new proof of Kastermans’ Theorem 1.1. This is worthwhile for severa ...

... the continuum hypothesis. In this paper we answer these questions in the positive: Theorem 1.2. The existence of a Π11 mcg is consistent with arbitrarily large continuum (assuming the consistency of ZFC). At the same time, we give a new proof of Kastermans’ Theorem 1.1. This is worthwhile for severa ...

Two Extensions of Conjoint Measurement1v2

... pose that the stimuli are pure tones and they are ordered by loudness, then given a tone and a intensity, it is well known that it is not always possible to select a frequency so that the resulting tone has a loudness equal to that of the given one. So it seems clear that we must weaken Condition (4 ...

... pose that the stimuli are pure tones and they are ordered by loudness, then given a tone and a intensity, it is well known that it is not always possible to select a frequency so that the resulting tone has a loudness equal to that of the given one. So it seems clear that we must weaken Condition (4 ...

Reachability and Connectivity Queries in Constraint Databases

... Both of these results follow from [4]. The inability to express connectedness is a crucial obstacle in applying these languages to geographic databases. Although connectivity is perhaps the most natural geometric property that is absent from rst-order constraint query languages, there are many othe ...

... Both of these results follow from [4]. The inability to express connectedness is a crucial obstacle in applying these languages to geographic databases. Although connectivity is perhaps the most natural geometric property that is absent from rst-order constraint query languages, there are many othe ...

On the quotient of a b-Algebra by a non closed b

... Now, we define the center of an associative q-algebra (E | F, m) as the kernel of the morphism m00 − m0 . And a q-algebra (E | F, m) is said to be commutative if m0 = m00 . Recall that if E | F is a quotient bornological space and E0 a b-subspace of E such that F is a b-subspace of E0 , the natural ...

... Now, we define the center of an associative q-algebra (E | F, m) as the kernel of the morphism m00 − m0 . And a q-algebra (E | F, m) is said to be commutative if m0 = m00 . Recall that if E | F is a quotient bornological space and E0 a b-subspace of E such that F is a b-subspace of E0 , the natural ...

Real banach algebras

... L. INGELSTAM,Real Banach algebras complex algebras is easy; many techniques valid for complex algebras will work in the real case as well (el. see. 2). Also since any real algebra can be embedded in a complex (see. 3), some general results can be obtained in this way from the complex case. In quite ...

... L. INGELSTAM,Real Banach algebras complex algebras is easy; many techniques valid for complex algebras will work in the real case as well (el. see. 2). Also since any real algebra can be embedded in a complex (see. 3), some general results can be obtained in this way from the complex case. In quite ...

Gundy`s decomposition for non-commutative martingales

... in L1 (M, τ ) has either a convergent or a 2-co-lacunary subsequence. The paper is organized as follows. In Section 1, we set some basic preliminary background concerning non-commutative symmetric spaces and martingale theory that will be needed throughout. Section 2 is devoted mainly to the stateme ...

... in L1 (M, τ ) has either a convergent or a 2-co-lacunary subsequence. The paper is organized as follows. In Section 1, we set some basic preliminary background concerning non-commutative symmetric spaces and martingale theory that will be needed throughout. Section 2 is devoted mainly to the stateme ...

MATH 436 Notes: Finitely generated Abelian groups.

... If |X| < ∞ then | ⊕x∈X Z/2Z| = 2|X| . Thus | ⊕y∈Y Z/2Z| is also finite and so |Y | < ∞ and 2|Y | = 2|X| which yields |X| = |Y | as desired. So it only remains to consider the case |X| = |Y | = ∞. Let Pf inite (X) = {S ⊂ X||S| < ∞} be the set of finite subsets of X. Then there is a bijection Θ : Pf i ...

... If |X| < ∞ then | ⊕x∈X Z/2Z| = 2|X| . Thus | ⊕y∈Y Z/2Z| is also finite and so |Y | < ∞ and 2|Y | = 2|X| which yields |X| = |Y | as desired. So it only remains to consider the case |X| = |Y | = ∞. Let Pf inite (X) = {S ⊂ X||S| < ∞} be the set of finite subsets of X. Then there is a bijection Θ : Pf i ...

On the existence of invariant probability measures for Borel actions

... [2]), every aperiodic Borel action of a countable group is generically compressible. It follows that any notion which characterizes the inexistence of invariant probability measures must hold generically of every aperiodic Borel action of a countable group. The following fact both generalizes Kechri ...

... [2]), every aperiodic Borel action of a countable group is generically compressible. It follows that any notion which characterizes the inexistence of invariant probability measures must hold generically of every aperiodic Borel action of a countable group. The following fact both generalizes Kechri ...

Appendix 3 - UCLA Department of Mathematics

... Proof. We first observe that it is enough to construct a ccc, dense, linear ordering (X; R) that is not separable. If we have such an (X; R), then we can let X 0 be the set of all Dedekind cuts in (X; R), i.e., the set of all bounded initial segments of (X; R) without R-greatest elements, and we can ...

... Proof. We first observe that it is enough to construct a ccc, dense, linear ordering (X; R) that is not separable. If we have such an (X; R), then we can let X 0 be the set of all Dedekind cuts in (X; R), i.e., the set of all bounded initial segments of (X; R) without R-greatest elements, and we can ...

DIPLOMAMUNKA

... We now recursively define the class of primitive recursive functions: PR1 The zero function, Z(x) = 0 for any x, is primitive recursive. PR2 The successor function S(x) is primitive recursive. PR3 For any natural numbers i, n such that 0 ≤ i < n, the projection function Pin (x0 , x1 , . . . , xn−1 ) ...

... We now recursively define the class of primitive recursive functions: PR1 The zero function, Z(x) = 0 for any x, is primitive recursive. PR2 The successor function S(x) is primitive recursive. PR3 For any natural numbers i, n such that 0 ≤ i < n, the projection function Pin (x0 , x1 , . . . , xn−1 ) ...

Berkovich spaces embed in Euclidean spaces - IMJ-PRG

... K was complete [Be1, Sections 3.4 and 3.5]. For a quasi-projective variety V over an arbitrary valued field K , there are two approaches to defining the topological space V an : 1. Use the same definition as for complete fields in [Be1], in terms of seminorms. 2. Use a definition as in [HL, Section ...

... K was complete [Be1, Sections 3.4 and 3.5]. For a quasi-projective variety V over an arbitrary valued field K , there are two approaches to defining the topological space V an : 1. Use the same definition as for complete fields in [Be1], in terms of seminorms. 2. Use a definition as in [HL, Section ...

Mathematical Problems and Games

... Type 1: We may shift u to the right or left one unit. Type 2: We may erase some O’s (or l’s) in u as long as the set of indices which are erased has frequency (or arithmetic density) zero. Type 3: We can change some entries from 0 to 1 (or 1 to 0) provided the set of entries has frequency 0. Type 4: ...

... Type 1: We may shift u to the right or left one unit. Type 2: We may erase some O’s (or l’s) in u as long as the set of indices which are erased has frequency (or arithmetic density) zero. Type 3: We can change some entries from 0 to 1 (or 1 to 0) provided the set of entries has frequency 0. Type 4: ...

# Banach–Tarski paradox

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them, without changing their shape. However, the pieces themselves are not ""solids"" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.A stronger form of the theorem implies that given any two ""reasonable"" solid objects (such as a small ball and a huge ball), either one can be reassembled into the other. This is often stated informally as ""a pea can be chopped up and reassembled into the Sun"" and called the ""pea and the Sun paradox"".The reason the Banach–Tarski theorem is called a paradox is that it contradicts basic geometric intuition. ""Doubling the ball"" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here, because in this case it is impossible to define the volumes of the considered subsets, as they are chosen with such a large porosity. Reassembling them reproduces a volume, which happens to be different from the volume at the start.Unlike most theorems in geometry, the proof of this result depends in a critical way on the choice of axioms for set theory. It can be proven using the axiom of choice, which allows for the construction of nonmeasurable sets, i.e., collections of points that do not have a volume in the ordinary sense, and whose construction requires an uncountable number of choices.It was shown in 2005 that the pieces in the decomposition can be chosen in such a way that they can be moved continuously into place without running into one another.