On supra λ-open set in bitopological space

... The closure and interior of asset A in (X,T) denoted by int(A), cl(A)respectively .A subset A is said to be α-set if A⊆int(cl(int(A))).a sub collection Ω⊂2x is called supra topological space [4 ] , the element of Ω are said to be supra open set in (X,Ω) and the complement of a supra open set is call ...

... The closure and interior of asset A in (X,T) denoted by int(A), cl(A)respectively .A subset A is said to be α-set if A⊆int(cl(int(A))).a sub collection Ω⊂2x is called supra topological space [4 ] , the element of Ω are said to be supra open set in (X,Ω) and the complement of a supra open set is call ...

More Functions Associated with Semi-Star-Open Sets

... Y. Since f is semi*-irresolute, by invoking Theorem 3.13, (h∘f )-1(V)=f -1(h-1(V)) is semi*-closed in X. Hence h∘f is contra-semi*-continuous. Theorem 3.24: Let f :X⟶Y be semi*-irresolute and h:Y⟶Z be contra-semi*-irresolute. Then h∘f: X⟶Z is contra-semi*-irresolute. Proof: Let V be a semi*-open set ...

... Y. Since f is semi*-irresolute, by invoking Theorem 3.13, (h∘f )-1(V)=f -1(h-1(V)) is semi*-closed in X. Hence h∘f is contra-semi*-continuous. Theorem 3.24: Let f :X⟶Y be semi*-irresolute and h:Y⟶Z be contra-semi*-irresolute. Then h∘f: X⟶Z is contra-semi*-irresolute. Proof: Let V be a semi*-open set ...

Archimedean Rankin Selberg Integrals

... representations π and π 0 . Anyway, by using this general result and by following Cogdell and Piatetski-Shapiro ([8]), it is shown that for the case (n, n − 1) and (n, n) the relevant L-factor is obtained in terms of vectors which are finite under the appropriate maximal compact subgroups. The resul ...

... representations π and π 0 . Anyway, by using this general result and by following Cogdell and Piatetski-Shapiro ([8]), it is shown that for the case (n, n − 1) and (n, n) the relevant L-factor is obtained in terms of vectors which are finite under the appropriate maximal compact subgroups. The resul ...

Groupoids in categories with pretopology

... which are the intersection of bibundle functors and bibundle actors. The categories of vague functors and bibundle functors are equivalent, and vague isomorphisms and bibundle equivalences are also equivalent notions; all the other types of morphisms are genuinely different and are useful in differe ...

... which are the intersection of bibundle functors and bibundle actors. The categories of vague functors and bibundle functors are equivalent, and vague isomorphisms and bibundle equivalences are also equivalent notions; all the other types of morphisms are genuinely different and are useful in differe ...

The local structure of algebraic K-theory

... As such, it is a meta-theme for mathematics, but the successful codification of this phenomenon in homotopy-theoretic terms is what has made algebraic K-theory into a valuable part of mathematics. For a further discussion of algebraic K-theory we refer the reader to chapter I below. Calculations of ...

... As such, it is a meta-theme for mathematics, but the successful codification of this phenomenon in homotopy-theoretic terms is what has made algebraic K-theory into a valuable part of mathematics. For a further discussion of algebraic K-theory we refer the reader to chapter I below. Calculations of ...

Global Aspects of Ergodic Group Actions Alexander S

... of (X, µ) by conjugation on A(Γ, X, µ) as well as the study of the global structure of the space of cocycles and certain canonical actions on it. Our goal here is to explore this point of view by presenting (a) earlier results, sometimes in new formulations or with new proofs, (b) new theorems, and ...

... of (X, µ) by conjugation on A(Γ, X, µ) as well as the study of the global structure of the space of cocycles and certain canonical actions on it. Our goal here is to explore this point of view by presenting (a) earlier results, sometimes in new formulations or with new proofs, (b) new theorems, and ...

1 Introduction

... properties and characterizations. In 1996, Keun [4] introduced fuzzy scontinuous, fuzzy s-open and fuzzy s-closed maps and established a number of characterizations. Now, we introduce the concept of supra α-open set, sα-continuous and investigate some of the basic properties for this class of functi ...

... properties and characterizations. In 1996, Keun [4] introduced fuzzy scontinuous, fuzzy s-open and fuzzy s-closed maps and established a number of characterizations. Now, we introduce the concept of supra α-open set, sα-continuous and investigate some of the basic properties for this class of functi ...

Metric geometry of locally compact groups

... example that defined by d(γ, γ 0 ) = 1 whenever γ, γ 0 are distinct. The three other classes can be characterized as follows. Proposition 1.A.1. Let Γ be a group. (ct) Γ is countable if and only if it has a left-invariant metric with finite balls. Moreover, if d1 , d2 are two such metrics, the ident ...

... example that defined by d(γ, γ 0 ) = 1 whenever γ, γ 0 are distinct. The three other classes can be characterized as follows. Proposition 1.A.1. Let Γ be a group. (ct) Γ is countable if and only if it has a left-invariant metric with finite balls. Moreover, if d1 , d2 are two such metrics, the ident ...

Full text

... The proof of Theorem 1.2 involves an inductive argument, where several cases have to be taken into account. We begin with two lemmas which link the floor expression of the statement (a so-called Beatty sequence) with the Fibonacci numbers. Lemma 2.1. Let n ≥ 4. Then (1) bnµc = F2k − 1 ⇔ n = F2k+1 − ...

... The proof of Theorem 1.2 involves an inductive argument, where several cases have to be taken into account. We begin with two lemmas which link the floor expression of the statement (a so-called Beatty sequence) with the Fibonacci numbers. Lemma 2.1. Let n ≥ 4. Then (1) bnµc = F2k − 1 ⇔ n = F2k+1 − ...

Topolog´ıa Algebraica de Espacios Topológicos Finitos y Aplicaciones

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...

# Brouwer fixed-point theorem

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f mapping a compact convex set into itself there is a point x0 such that f(x0) = x0. The simplest forms of Brouwer's theorem are for continuous functions f from a closed interval I in the real numbers to itself or from a closed disk D to itself. A more general form than the latter is for continuous functions from a convex compact subset K of Euclidean space to itself.Among hundreds of fixed-point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics.In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem and the Borsuk–Ulam theorem.This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep results about differential equations and is covered in most introductory courses on differential geometry.It appears in unlikely fields such as game theory. In economics, Brouwer's fixed-point theorem and its extension, the Kakutani fixed-point theorem, play a central role in the proof of existence of general equilibrium in market economies as developed in the 1950s by economics Nobel prize winners Kenneth Arrow and Gérard Debreu.The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.Proving results such as the Poincaré–Bendixson theorem requires the use of topological methods.This work at the end of the 19th century opened into several successive versions of the theorem. The general case was first proved in 1910 by Jacques Hadamard and by Luitzen Egbertus Jan Brouwer.