p. 199 - 208 On some ordinary and fuzzy homogenity types S. Al Ghour and K. Al-Zoubi Received: March 6, 2007; Revised: April 20, 2008; Accepted: April 22, 2008 Abstract. Finite SLH topological spaces are characterized as partition topological spaces. As a consequence, two partial answers for a question raised in [3] are obtained. Closed-homogeneous topological spaces are characterized. Having a minimal open set is proved to be a sufficient condition for a homogeneous topological space to be closed-homogeneous. Closed-homogeneity is extended to include fuzzy topological spaces as a "good extension" according to Lowen's sense of closed-homogeneity in ordinary topological spaces. It is proved that homogeneity and closed-homogeneity in fuzzy topological spaces are equivalent under some conditions. Various open questions are also given. Keywords: homogeneity; strong local homogeneity; local homogeneity; closed homogeneity; generated topologies. AMS Subject classification: Primary: 54A40. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |