On Tychonoff-type Hypertopologies

G. Dimov, F. Obersnel, G. Tironi

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. We give some results on  Tychonoff-type topologies on an arbitrary family M  of subsets of a set X; in particular,  a description of all Tychonoff-type topologies  O  on M  is given when M  contains all singletons.