On a class of transformation groups
... subgroupof G. In particular, if G and II have the same underlyinggroup and the same one-parameter subgroups,theyare identical. The followingpropositionfollows directlyfrom 1,2, 1. 5, and the (lefinitionof a Lie topology. 1. 6. PROPOSITION. A groupof homeomorphisms of a topologicalspace admits at mos ...
... subgroupof G. In particular, if G and II have the same underlyinggroup and the same one-parameter subgroups,theyare identical. The followingpropositionfollows directlyfrom 1,2, 1. 5, and the (lefinitionof a Lie topology. 1. 6. PROPOSITION. A groupof homeomorphisms of a topologicalspace admits at mos ...
An Injectivity Theorem for Casson
... field of characteristic zero. If α factors through a p-group, then Id ⊗f : Q[H]k ⊗Z[π] M → Q[H]k ⊗Z[π] N is also injective. This theorem (sometimes with the special case that H is the trivial group) is at the heart of many results in link concordance. We refer to the work of Cha, Friedl, Ko, Levine ...
... field of characteristic zero. If α factors through a p-group, then Id ⊗f : Q[H]k ⊗Z[π] M → Q[H]k ⊗Z[π] N is also injective. This theorem (sometimes with the special case that H is the trivial group) is at the heart of many results in link concordance. We refer to the work of Cha, Friedl, Ko, Levine ...
Decompositions of normality and interrelation among its variants
... It turns out that the set Auθ is the smallest θ-closed set containing A. Above discussed uθ-closure operator is the closure operator in the θ-topology [τθ for the space (X, τ )]. Theorem 2.11. For a topological space X, the following statements are equivalent (1) X is nearly normal. (2) For every pa ...
... It turns out that the set Auθ is the smallest θ-closed set containing A. Above discussed uθ-closure operator is the closure operator in the θ-topology [τθ for the space (X, τ )]. Theorem 2.11. For a topological space X, the following statements are equivalent (1) X is nearly normal. (2) For every pa ...
1980 Mathematical Subject Classification Code. 54A20
... essentially compact if NX is a finite set; this terminology is due to ...
... essentially compact if NX is a finite set; this terminology is due to ...
Some Types Of Compactness Via Ideal
... (resp., β-continuous) surjection and (X, τ, I) is βIcompact, then (Y, σ, f(I)) is βf(I)-compact (resp., f(I)compact). Proof Let {V λ : λ∈Λ} be a β-open (resp., open) cover of Y. Then {f-1(V λ ) : λ∈Λ} is a β-open cover of X and hence there exists a finite subset Λ 0 of Λ such that X{f-1(V λ ) : λ∈Λ ...
... (resp., β-continuous) surjection and (X, τ, I) is βIcompact, then (Y, σ, f(I)) is βf(I)-compact (resp., f(I)compact). Proof Let {V λ : λ∈Λ} be a β-open (resp., open) cover of Y. Then {f-1(V λ ) : λ∈Λ} is a β-open cover of X and hence there exists a finite subset Λ 0 of Λ such that X{f-1(V λ ) : λ∈Λ ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.