On two classes of sets containing all Baire sets and all co-analytic sets

Zoltan Balogh; Harold Bennett

doi:10.1016/0166-8641(89)90106-5

On two classes of sets containing all Baire sets and all co-analytic sets

Zoltan Balogh, Harold Bennett

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The notions of an S_δ set and an R_δ set are introduced. A space is S-perfect (R-perfect) if each closed set is an S_δ set (R_δ) set. Conditions are given which indicate when spaces are S-perfect or R-perfect. Examples are given of spaces which do not have these properties and examples are given of spaces with these properties that are not perfect spaces. The images of S-perfect and R-perfect spaces under various types of mappings are investigated.

Original language	English
Pages (from-to)	247-264
Number of pages	18
Journal	Topology and its Applications
Volume	33
Issue number	3
DOIs	https://doi.org/10.1016/0166-8641(89)90106-5
State	Published - Nov 1989

Keywords

Baire sets
R-perfect
S-perfect
co-analytic sets
open-compact maps
perfect maps
perfect sets

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10.1016/0166-8641(89)90106-5

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AB - The notions of an Sδ set and an Rδ set are introduced. A space is S-perfect (R-perfect) if each closed set is an Sδ set (Rδ) set. Conditions are given which indicate when spaces are S-perfect or R-perfect. Examples are given of spaces which do not have these properties and examples are given of spaces with these properties that are not perfect spaces. The images of S-perfect and R-perfect spaces under various types of mappings are investigated.

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KW - S-perfect

KW - co-analytic sets

KW - open-compact maps

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On two classes of sets containing all Baire sets and all co-analytic sets

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