ScholarLens Back to search
1998•Proceedings of the American Mathematical SocietyOpen access

Neither first countable nor Cech-complete spaces are maximal Tychonoff connected

Dmitri B. Shakhmatov, Michael G. Tkačenko, Vladimir V. Tkachuk, Stephen W. Watson, Richard G. Wilson

Open full text 12 citations

Abstract

A connected Tychonoff space X X is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on X X . We show that if X X is a connected Tychonoff space and X ∈ { X\in \{ locally separable spaces, locally Čech-complete spaces, first countable spaces } \} , then X X is not maximal Tychonoff connected. This result is new even in the cases where X X is compact or metrizable.

Open-access reader

About this research paper

What this paper is about

A connected Tychonoff space X X is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on X X . We show that if X X is a connected Tychonoff space and X ∈ { X\in \{ locally separable spaces, locally Čech-complete spaces, first countable spaces } \} , then X X is not maximal Tychonoff connected. This result is new even in the cases where X X is compact or metrizable.

Why it matters

OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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

A connected Tychonoff space X X is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on X X . We show that if X X is a connected Tychonoff space and X ∈ { X\in \{ locally separable spaces, locally Čech-complete spaces, first countable spaces } \} , then X X is not maximal Tychonoff connected. This result is new even in the cases where X X is compact or metrizable.

Key concepts: Countable set, Tychonoff space, Mathematics, Discrete mathematics, Pure mathematics, Combinatorics, Topological space

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Neither first countable nor Cech-complete spaces are maximal Tychonoff connected — Research Paper | ScholarLens