Completely N-continuous Multifunctions
... Theorem 12. Let F : X → Y be a multifunction from a topological space (X, τ ) to a topological space (Y, υ) and let F (X) be endowed with subspace topology. If F is upper completely N-continuous, then F : X → F (X) is upper completely N-continuous. Proof. Since F is upper completely N-continuous, F ...
... Theorem 12. Let F : X → Y be a multifunction from a topological space (X, τ ) to a topological space (Y, υ) and let F (X) be endowed with subspace topology. If F is upper completely N-continuous, then F : X → F (X) is upper completely N-continuous. Proof. Since F is upper completely N-continuous, F ...
Uniformities and uniformly continuous functions on locally
... the SIN property is that every left uniformly continuous real-valued function on G is right uniformly continuous (and vice versa). Rather surprisingly, it is still unknown if the converse holds true. OPEN QUESTION. (Itzkowitz, [5]) Is a topological group G SIN whenever every left uniformly continuou ...
... the SIN property is that every left uniformly continuous real-valued function on G is right uniformly continuous (and vice versa). Rather surprisingly, it is still unknown if the converse holds true. OPEN QUESTION. (Itzkowitz, [5]) Is a topological group G SIN whenever every left uniformly continuou ...
co-γ-Compact Generalized Topologies and c
... Aı ∈ c (gγ ) for ı ∈ I. Then we have the following posibilities: (a) If Aı ∈ c (τ ) for each ı ∈ I, then A ∈ c (τ ) ⊂ c (gγ ) since c (τ ) is a topology. (b) If Aı ∈ c (gγ ) − c (τ ) for each ı ∈ I, then Aı ∈ gγ − τ for each ı ∈ I. Thus A ∈ τ or A ∈ gγ − τ. If A ∈ τ, choose an ı ∈ I, then Aı ∈ gγ − ...
... Aı ∈ c (gγ ) for ı ∈ I. Then we have the following posibilities: (a) If Aı ∈ c (τ ) for each ı ∈ I, then A ∈ c (τ ) ⊂ c (gγ ) since c (τ ) is a topology. (b) If Aı ∈ c (gγ ) − c (τ ) for each ı ∈ I, then Aı ∈ gγ − τ for each ı ∈ I. Thus A ∈ τ or A ∈ gγ − τ. If A ∈ τ, choose an ı ∈ I, then Aı ∈ gγ − ...
![Forms [14 CM] and [43 W] through [43 AC] [14 CM] Kolany`s](http://s1.studyres.com/store/data/014889156_1-4ddf6cb6c42621168d150358ab1c3978-300x300.png)
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.