Nayar, Bhamini M. P.; Arya, S. P. Semi-topological properties. (English) Zbl 0765.54002 Int. J. Math. Math. Sci. 15, No. 2, 267-272 (1992). Summary: A property preserved under a semi-homeomorphism is said to be a semi- topological property. We prove the following results: (1) A topological property \(P\) is semi-topological if and only if the statement “\((X,{\mathcal T})\) has \(P\) if and only if \((X,F({\mathcal T}))\) has \(P\)” is true where \(F({\mathcal T})\) is the finest topology on \(X\) having the same family of semi-open sets as \((X,{\mathcal T})\). (2) If \(P\) is a topological property being minimal \(P\) is semi-topological if and only if for each minimal \(P\) space \((X,{\mathcal T})\), \({\mathcal T}=F({\mathcal T})\). Cited in 2 Documents MSC: 54A05 Topological spaces and generalizations (closure spaces, etc.) 54D25 “\(P\)-minimal” and “\(P\)-closed” spaces Keywords:semi-topological property PDFBibTeX XMLCite \textit{B. M. P. Nayar} and \textit{S. P. Arya}, Int. J. Math. Math. Sci. 15, No. 2, 267--272 (1992; Zbl 0765.54002) Full Text: DOI EuDML