A remark on \(\Theta\)-regular spaces. (English) Zbl 0888.54027

Kovár, Martin M.

Int. J. Math. Math. Sci. 21, No. 1, 199-200 (1998).

Summary: An embedding characterization of \(\theta\)-regularity using the Wallman-type compactification is given. The productivity of \(\theta\)-regularity and a slight generalization of Nagami’s product theorem to non-Hausdorff paracompact \(\Sigma\)-spaces are obtained as a corollary.

MSC:

54D35	Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54B10	Product spaces in general topology
54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)

Keywords:

paracompact \(\Sigma\)-space; \(\theta\)-regularity; Wallman-type compactification