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.
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$\begingroup$ Dear @Vahideh: Please do not use the deprecated tag 'topology'. The tag 'gn.general-topology' is sufficient. $\endgroup$– Ricardo AndradeCommented Sep 30, 2013 at 14:01
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$\begingroup$ Ok dear.But why I do it? $\endgroup$– Vahideh BagheriCommented Sep 30, 2013 at 20:08
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$\begingroup$ 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 AndradeCommented Sep 30, 2013 at 20:13
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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.
