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Sanabria, José Eduardo; Rosas, Ennis; Blanco, Clara

Properties of nearly \(S\)-paracompact spaces. (English) Zbl 1520.54013

Proyecciones 42, No. 1, 91-103 (2023).
K. Y. Al-Zoubi [Acta Math. Hung. 110, No. 1–2, 165–174 (2006; Zbl 1103.54015)] introduced a weaker version of paracompact spaces called \(S\)-paracompact spaces, which are spaces in which every open cover of the space has a locally finite semi-open refinement. The authors of this paper study some basic properties of nearly \(S\)-paracompact spaces and their characterization under certain hypotheses about the spaces. They establish relationships between this class of spaces and nearly paracompact spaces, \(S\)-paracompact spaces, almost paracompact spaces, nearly compact spaces, countably \(S\)-closed spaces and \(S\)-closed spaces. Finally, they study the invariance of nearly \(S\)-paracompact spaces under direct and inverse images of pre-semi-open, almost completely continuous, almost closed, almost continuous, regular open and \(S\)-continuous functions.
Reviewer: Francisco Gallego Lupiáñez (Madrid)

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)
54F65 Topological characterizations of particular spaces
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.
54C10 Special maps on topological spaces (open, closed, perfect, etc.)

Keywords:

semi-open set; nearly \(S\)-paracompact space; semiregular space; pre-semi-open function; almost closed function

Citations:

Zbl 1103.54015
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Full Text: DOI

References:

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