## Tsukuba Journal of Mathematics

### Local properties and maximal Tychonoff connected spaces

#### Abstract

We prove that, if $X$ is a Tychonoff connected space and $\chi (x, X) \leq \omega$ for some $x \in X$, then there exists a strictly stronger Tychonoff connected topology on the space $X$, i.e., the space $X$ is not maximal Tychonoff connected. We also establish that if X is locally connected or CT-compact or has pointwise countable type then $X$ cannot be maximal Tychonoff connected.

#### Article information

Source
Tsukuba J. Math., Volume 30, Number 2 (2006), 241-257.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165063

Digital Object Identifier
doi:10.21099/tkbjm/1496165063

Mathematical Reviews number (MathSciNet)
MR2271300

Zentralblatt MATH identifier
1118.54004

#### Citation

Mill, Jan van; Tkachenko, Mikhail G.; Tkachuk, Vladimir V. Local properties and maximal Tychonoff connected spaces. Tsukuba J. Math. 30 (2006), no. 2, 241--257. doi:10.21099/tkbjm/1496165063. https://projecteuclid.org/euclid.tkbjm/1496165063