On Some Generalization of Paracompactness

The generalization of paracompact spaces via so-sets, sets are unions of open and nowhere dense sets, was studied. The aim of this paper is to establish the relationship between so-paracompact spaces and other generalizations of paracompact spaces and clarify the conditions under which the so-paracompact space is compact. The problem is solved by methods of general topology. It is proved that the sequentially compact so-paracompact space is compact. It is proved that the so-paracompactness saved when multiplied by the compact. Previously, other authors introduced the concept of S-paracompact space, based on the semi-open sets. Class of so-paracompact spaces wider than the class S-paracompact spaces. This paper shows that there are so-paracompact spaces which are not S-paracompact.

so-set, so-paracompact space, S-paracompact space, sequen-tially compact space