Mathematics – General Topology
Scientific paper
2002-04-10
Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 51--70, Topology Atlas, Toronto, 2002
Mathematics
General Topology
20 pages
Scientific paper
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new topology, calling it Tychonoff-type topology. The present paper is devoted to a detailed study of Tychonoff-type topologies on an arbitrary family M of subsets of a set X. When M contains all singletons, a description of all Tychonoff-type topologies O on M is given. The continuous maps of a special form between spaces of the type (M,O) are described in an isomorphism theorem. The problem of commutability between hyperspaces and subspaces with respect to a Tychonoff-type topology} is investigated as well. Some topological properties of the hyperspaces (M,O) with Tychonoff-type topologies O are briefly discussed.
Dimov Georgi
Obersnel Franco
Tironi Gino
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