Abstract
A topological space X role=presentation> X X X is called C role=presentation> C C C - paracompact if there exist a paracompact space Y role=presentation> Y Y Y and a bijective function f : X ⟶ Y role=presentation> f : X ⟶ Y f : X ⟶ Y f:X\longrightarrow Y such that the restriction f | A : A ⟶ f ( A ) role=presentation> f | A : A ⟶ f ( A ) f | A : A ⟶ f ( A ) f|_{A}:A\longrightarrow f(A) is a homeomorphism for each compact subspace A ⊆ X role=presentation> A ⊆ X A ⊆ X A\subseteq X . A topological space X role=presentation> X X X is called C 2 role=presentation> C 2 C 2 C_2 - paracompact if there exist a Hausdorff paracompact space Y role=presentation> Y Y Y and a bijective function f : X ⟶ Y role=presentation> f : X ⟶ Y f : X ⟶ Y f:X\longrightarrow Y such that the restriction f | A : A ⟶ f ( A ) role=presentation> f | A : A ⟶ f ( A ) f | A : A ⟶ f ( A ) f|_{A}:A\longrightarrow f(A) is a homeomorphism for each compact subspace A ⊆ X role=presentation> A ⊆ X A ⊆ X A\subseteq X . We investigate these two properties and produce some examples to illustrate the relationship between them and C role=presentation> C C C -normality, minimal Hausdorff, and other properties.
Highlights
We introduce two new topological properties, C -paracompactness and C2 -paracompactness
The purpose of this paper is to investigate these two properties
V is coarser than the usual ordered topology on ω1 and (ω1, V) is a Hausdorff compact space because it is homeomorphic to ω1 + 1
Summary
We introduce two new topological properties, C -paracompactness and C2 -paracompactness. The purpose of this paper is to investigate these two properties. Throughout this paper, we denote an ordered pair by ⟨x, y⟩ , the set of positive integers by N, the rational numbers by Q, the irrational numbers by P , and the set of real numbers by R. A T4 space is a T1 normal space and a Tychonoff space (
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