We investigate these two properties and produce some examples to illustrate the relationship between them and C -normality, minimal Hausdorff, and other properties.
📌 3 Key Takeaways
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Objective & Hypothesis:A topological space X is called C -paracompact if there exist a paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X .
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Key Findings & Data:A topological space X is called C2 -paracompact if there exist a Hausdorff paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X .
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Conclusion & Impact:We investigate these two properties and produce some examples to illustrate the relationship between them and C -normality, minimal Hausdorff, and other properties.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
A topological space X is called C -paracompact if there exist a paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . A topological space X is called C2 -paracompact if there exist a Hausdorff paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . We investigate these two properties and produce some examples to illustrate the relationship between them and C -normality, minimal Hausdorff, and other properties.
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Cite This Article
SAEED, M. M., KALANTAN, L., ALZUMI, H. (2022). C-Paracompactness and $C_2$-paracompactness. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 9–20. https://ajindex.com/articles/607968
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