关于L-半拓扑空间的一些注记

Some Notes on L-Semi Topological Space

本文首先类比上半拓扑与下半拓扑引入左半拓扑与右半拓扑概念。然后,集中讨论左半拓扑(即,L-半拓扑)空间的点集理论,获得了该类半拓扑空间的基本点集性质、子空间性质和网收敛性质。进而,使拓扑空间的基本性质得到推广。同时,也通过反例举出了在拓扑空间成立而在L-半拓扑空间不成立的一些结果。

Firstly, the concepts of both Left-semi topology and Right-semi topology are introduced by means of both sup-semi-topology and inf-semi-topology. Then, the point set theory of Left-semi-topological (i.e., L-semi-topological) spaces is discussed. Some results on basic point sets, the properties of sub-spaces and the convergence of the net are obtained on L-semi-topological spaces. Furthermore, some basic properties of topological spaces are generalized, and it is cited by counterexamples that some results are not true on a L-semi topological space, but they are correct on topological spaces.