# Is there a maximal (or maximal Tychonoff) non normal space?

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.

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