关于Tychonoff型超拓扑
On Tychonoff-type hypertopologies
摘要：
1975年，M. M. Choban在拓扑空间的所有闭子集的集合上引入了一个新的拓扑，它类似于Tychonoff拓扑，但比它弱。Dimov和D. Vakarelov使用了这个新拓扑的推广版本，称之为吉洪诺夫型拓扑。本文研究了集合X的任意子集族M上的Tychonoff型拓扑。当M包含所有单例时，给出了M上所有Tychonoff型拓扑O的描述。用同构定理描述了（M，O）型空间之间特殊形式的连续映射。研究了超空间和子空间关于Tychonoff型拓扑的可积性问题。讨论了具有Tychonoff型拓扑O的超空间（M，O）的一些拓扑性质。
英文摘要：
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.
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