bc-continuous function
... Hence there is a finite subset F of X such that X W : i F ,therefore X is b-compact. So A is b-compact set . 2.12 Theorem Let Y be C1 - space , then a function f : X Y is bc-continuous if and only if f is H-continuous . Proof :Let f : X Y is bc-continuous, such that Y is C1 - space ...
... Hence there is a finite subset F of X such that X W : i F ,therefore X is b-compact. So A is b-compact set . 2.12 Theorem Let Y be C1 - space , then a function f : X Y is bc-continuous if and only if f is H-continuous . Proof :Let f : X Y is bc-continuous, such that Y is C1 - space ...
Some separation axioms in L-topological spaces
... Theorem 2.3. Let (LX , δ) be a sub-T2 space, then for each molecular net S such that |KS | ≤ 1, where KS = {x ∈ X : lim S(x) = >}. Proof. Let (LX , δ) be a sub-T2 space and S = {S(n) : n ∈ D} be a molecular net. Assume that |KS | ≥ 2, for any x, y ∈ KS with x 6= y, since (LX , δ) is sub-T2 , there e ...
... Theorem 2.3. Let (LX , δ) be a sub-T2 space, then for each molecular net S such that |KS | ≤ 1, where KS = {x ∈ X : lim S(x) = >}. Proof. Let (LX , δ) be a sub-T2 space and S = {S(n) : n ∈ D} be a molecular net. Assume that |KS | ≥ 2, for any x, y ∈ KS with x 6= y, since (LX , δ) is sub-T2 , there e ...
http://www.math.uni-muenster.de/u/lueck/publ/lueck/surveyclassi04.pdf
... Group means always locally compact Hausdorff topological group with a countable base for its topology. Definition 1. (G-CW -complex) A G-CW complex X is a G-space together with a G-invariant filtration ∅ = X−1 ⊆ X0 ⊆ . . . ⊆ Xn ⊆ . . . ⊆ ...
... Group means always locally compact Hausdorff topological group with a countable base for its topology. Definition 1. (G-CW -complex) A G-CW complex X is a G-space together with a G-invariant filtration ∅ = X−1 ⊆ X0 ⊆ . . . ⊆ Xn ⊆ . . . ⊆ ...
Rz-SUPERCONTINUOUS FUNCTIONS 1. Introduction Strong forms
... functions properly contains the class of Rcl -supercontinuous functions [35] which in its turn strictly contains the class of cl-supercontinuous (≡ clopen continuous) functions [28], [30] and is properly contained in the class of Rδ -supercontinuous functions [21] which is strictly contained in the ...
... functions properly contains the class of Rcl -supercontinuous functions [35] which in its turn strictly contains the class of cl-supercontinuous (≡ clopen continuous) functions [28], [30] and is properly contained in the class of Rδ -supercontinuous functions [21] which is strictly contained in the ...
GRAPH TOPOLOGY FOR FUNCTION SPACES(`)
... a beginning, it is advisable to consider first a subfamily of noncontinuous functions which, in a certain sense, can be approximated by continuous functions. One such subfamily consists of almost continuous functions which were introduced by Stallings [6]. An almost continuous function is one whose ...
... a beginning, it is advisable to consider first a subfamily of noncontinuous functions which, in a certain sense, can be approximated by continuous functions. One such subfamily consists of almost continuous functions which were introduced by Stallings [6]. An almost continuous function is one whose ...
G_\delta$-Blumberg spaces - PMF-a
... Proof. ⇒:Let U be a Gδ -B. space. Suppose g ∈ F (A). Since U is a Gδ -B. space and g|U ∈ F (U ), there exists a B ∈ DG(U) such that g|B ∈ C(B). Since U is a Gδ in X, B is a Gδ and dense subset of A. Therefore A is a Gδ -B. space. ⇐: Suppose A is a Gδ -B. space and g ∈ F (U ). We can extend g to a fu ...
... Proof. ⇒:Let U be a Gδ -B. space. Suppose g ∈ F (A). Since U is a Gδ -B. space and g|U ∈ F (U ), there exists a B ∈ DG(U) such that g|B ∈ C(B). Since U is a Gδ in X, B is a Gδ and dense subset of A. Therefore A is a Gδ -B. space. ⇐: Suppose A is a Gδ -B. space and g ∈ F (U ). We can extend g to a fu ...
Section 21. The Metric Topology (Continued) - Faculty
... Note. We will see in Example 3 of Section 28 a set A = SΩ in a space X = S Ω where A has a limit point x = Ω, but there is no sequence of elements of A which converge to x = Ω. We will be able to conclude that this space is not metrizable. This might strike you as surprising that there is a differen ...
... Note. We will see in Example 3 of Section 28 a set A = SΩ in a space X = S Ω where A has a limit point x = Ω, but there is no sequence of elements of A which converge to x = Ω. We will be able to conclude that this space is not metrizable. This might strike you as surprising that there is a differen ...
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.