Haar null and Haar meager sets: a survey and
... lots of papers were published which either study some property of Haar null sets or use this notion of smallness to state facts which are true for almost every element of some structure. It was relatively easy to generalize this notion to non-abelian groups, on the other hand, the assumption that th ...
... lots of papers were published which either study some property of Haar null sets or use this notion of smallness to state facts which are true for almost every element of some structure. It was relatively easy to generalize this notion to non-abelian groups, on the other hand, the assumption that th ...
Locally normal subgroups of totally disconnected groups. Part II
... • locally h.j.i.: We have LN (G) = {0, ∞}, or equivalently, every compact open subgroup of G is hereditarily just-infinite (h.j.i.), where a profinite group is said to be h.j.i. if every non-trivial closed locally normal subgroup is open. • atomic type: |LN (G)| > 2 but LC(G) = {0, ∞}, there is a un ...
... • locally h.j.i.: We have LN (G) = {0, ∞}, or equivalently, every compact open subgroup of G is hereditarily just-infinite (h.j.i.), where a profinite group is said to be h.j.i. if every non-trivial closed locally normal subgroup is open. • atomic type: |LN (G)| > 2 but LC(G) = {0, ∞}, there is a un ...
Fuzzy Irg- Continuous Mappings
... we have obtained a finite fuzzy Irg -open sub cover of A. Therefore A is fuzzy IRGO-compect relative to X. Theorem 3.9: A fuzzy Irg -continuous image of a fuzzy IRGO-compact fuzzy ideal topological space is fuzzy compact. Proof: Let f: (X, τ, I)→(Y, ) be a fuzzy Irg -continuous mapping from a fuzzy ...
... we have obtained a finite fuzzy Irg -open sub cover of A. Therefore A is fuzzy IRGO-compect relative to X. Theorem 3.9: A fuzzy Irg -continuous image of a fuzzy IRGO-compact fuzzy ideal topological space is fuzzy compact. Proof: Let f: (X, τ, I)→(Y, ) be a fuzzy Irg -continuous mapping from a fuzzy ...
PDF version - University of Warwick
... pi+1 − pi ≤ 1. Intersection homology (cf [2, page 138]) is defined exactly like singular permutation homology with dπi,j replaced by i + j − n + pn−j . However by using simplicial homology it can be seen that the intersection of an i–cycle with a j –dimensional PL subset can always be assumed to hav ...
... pi+1 − pi ≤ 1. Intersection homology (cf [2, page 138]) is defined exactly like singular permutation homology with dπi,j replaced by i + j − n + pn−j . However by using simplicial homology it can be seen that the intersection of an i–cycle with a j –dimensional PL subset can always be assumed to hav ...
Formal Algebraic Spaces
... is a homeomorphism onto the set of open prime ideals of A. This motivates the definition Spf(A) = {open prime ideals p ⊂ A} endowed with the topology coming from Spec(A). For each λ we can consider the structure sheaf OSpec(A/Iλ ) as a sheaf on Spf(A). Let Oλ be the corresponding pseudo-discrete she ...
... is a homeomorphism onto the set of open prime ideals of A. This motivates the definition Spf(A) = {open prime ideals p ⊂ A} endowed with the topology coming from Spec(A). For each λ we can consider the structure sheaf OSpec(A/Iλ ) as a sheaf on Spf(A). Let Oλ be the corresponding pseudo-discrete she ...
RELATIVE RIEMANN-ZARISKI SPACES 1. Introduction Let k be an
... Let us describe briefly other parts of the paper. In section 1.1 below, we recall Nagata compactification and Thomason’s noetherian approximation theorems, see [Nag] and [TT], C.9, and prove a slight generalization of the second theorem. Then we notice that the decomposition theorem is essentially e ...
... Let us describe briefly other parts of the paper. In section 1.1 below, we recall Nagata compactification and Thomason’s noetherian approximation theorems, see [Nag] and [TT], C.9, and prove a slight generalization of the second theorem. Then we notice that the decomposition theorem is essentially e ...
pdf
... b-closedness in terms of supra b-open set and supra b-closed set, respectively. Now, we introduce the concept of supra pre-open sets and study some basic properties of it. Also, we introduce the concepts of supra pre-continuous maps, supra pre-open maps and supra pre-closed maps and investigate seve ...
... b-closedness in terms of supra b-open set and supra b-closed set, respectively. Now, we introduce the concept of supra pre-open sets and study some basic properties of it. Also, we introduce the concepts of supra pre-continuous maps, supra pre-open maps and supra pre-closed maps and investigate seve ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.