ScholarLens Back to search
1979•Proceedings of the American Mathematical SocietyOpen access

Nonperfect Spaces with Point-Countable Bases

Peter Maxwell Davies

Open full text 0 citations

Abstract

We construct a completely regular space of cardinality ${\aleph _1}$ with a point-countable base, which is not perfect. This answers a question of Fleissner and Reed. We also construct, under the hypothesis ${2^{{\aleph _0}}} < {2^{{\aleph _1}}}$, a hereditarily normal space of cardinality ${\aleph _1}$ with a $\sigma$-disjoint base, which is not perfect.

Open-access reader

About this research paper

What this paper is about

We construct a completely regular space of cardinality ${\aleph _1}$ with a point-countable base, which is not perfect. This answers a question of Fleissner and Reed. We also construct, under the hypothesis ${2^{{\aleph _0}}} < {2^{{\aleph _1}}}$, a hereditarily normal space of cardinality ${\aleph _1}$ with a $\sigma$-disjoint base, which is not perfect.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We construct a completely regular space of cardinality ${\aleph _1}$ with a point-countable base, which is not perfect. This answers a question of Fleissner and Reed. We also construct, under the hypothesis ${2^{{\aleph _0}}} < {2^{{\aleph _1}}}$, a hereditarily normal space of cardinality ${\aleph _1}$ with a $\sigma$-disjoint base, which is not perfect.

Key concepts: Aleph, Countable set, Cardinality (data modeling), Disjoint sets, Construct (python library), Base (topology), Space (punctuation), Mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Nonperfect Spaces with Point-Countable Bases — Research Paper | ScholarLens