2
$\begingroup$

Is there a maximal (or maximal Tychonoff) non normal space? In "A Problem of Set-Teoretic Topology" the existence of a maximal Tychonoff space is asserted. Also there exists a perfectly normal maximal spaces (it suffices to consider a maximal topology on a countable set). Maximal topology means a maximal topology on a set which is devoid of isolated points. Maximal $\cal{P}$ space is a maximal space which hes the property $\cal{P}$ and is devoid of isolated points. If there is a relative article I would be grateful introduce it.

$\endgroup$
  • $\begingroup$ Dear @Vahideh: Please do not use the deprecated tag 'topology'. The tag 'gn.general-topology' is sufficient. $\endgroup$ – Ricardo Andrade Sep 30 '13 at 14:01
  • $\begingroup$ Ok dear.But why I do it? $\endgroup$ – Vahideh Bagheri Sep 30 '13 at 20:08
  • $\begingroup$ The use of certain tags, such as 'topology', is discouraged because the tags are not specific enough or because they duplicate other tags. $\endgroup$ – Ricardo Andrade Sep 30 '13 at 20:13
2
$\begingroup$

Malykhin constructed a consistent example of a Tychonoff non-normal maximal space in this paper:

V. I. Malykhin, "Extremally disconnected and similar groups", Soviet Math. Dokl. 16 (1975), 21–25.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.