SI_(2)-拟代数空间

SI_(2)-quasialgebraic spaces

在T_(0)空间上引入了SI_(2)-代数空间和SI_(2)-拟代数空间的概念,讨论了它们的一些性质,证明了:(1)一个T_(0)空间(X,τ)为SI_(2)-代数的当且仅当(X,τSI_(2))为B-空间;(2)一个T_(0)空间(X,τ)为SI_(2)-拟代数的当且仅当(X,τSI_(2))为超紧基空间;(3)一个T_(0)空间(X,τ)为SI_(2)-代数的当且仅当(X,τ)为交SI_(2)-连续和SI_(2)-拟代数的。

In this paper,the concepts of SI_(2)-algebraic spaces and SI_(2)-quasialgebraic spaces were introduced in T_(0) spaces.Some properties of them were investigated.It were proved that:(1)a T_(0) space(X,τ)is SI_(2)-algebraic iff(X,τSI_(2))is a B-space;(2)a T_(0) space(X,τ)is SI_(2)-quasialgebraic iff(X,τSI_(2))is a supercompactly based space;(3)a T_(0) space(X,τ)is SI_(2)-algebraic iff it is a meet SI_(2)-continuous and SI_(2)-quasialgebraic space.