Abstract

SOBERANO-GONZALEZ, I. E.; DELGADILLO-PINON, G.  and  ROJAS-HERNANDEZ, R.. Some topological properties of C-normality. Integración - UIS [online]. 2020, vol.38, n.2, pp.93-102.  Epub June 30, 2020. ISSN 0120-419X.  https://doi.org/10.18273/revint.v38n2-2020002.

A topological space X is C-normal if there exists a bijective function f: X → Y , for some normal space Y , such that the restriction f ↾C: C → f(C) is a homeomorphism for each compact C ⊂ X. The purpose of this work is to extend the known classes of C-normal spaces and clarify the behavior of C-normality under several usual topological operations; in particular, it is proved that C-normality is not preserved under closed subspaces, unions, continuous and closed images, and inverse images under perfect functions. These results are used to answer some questions raised in [1], [2] and [6].

Keywords : Normality; local compactness; epi-normality; compactness.

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