L-拓扑空间的次分离性公理

Sub-separation Axioms on L-topological Spaces

在L-拓扑空间中引入称之为次分离的分离性公理,包括次T1、次T2、次T212、次T3、次T4分离性等。新的分离性公理体系协调性很好,具有预期好的性质,如:具有遗传性和可乘性,是Low en意义下“L-好的推广”,和在次T2空间中分子网收敛在一定意义下唯一等。此外,文中还初步讨论了次分离性与文献中其它分离性的关系。

In this paper, we introduce the sub-separation axioms of L-topological spaces including sub-T1, sub-T2, sub-T21/2, sub-T3 and sub-T4. These new sub-separation axioms are harmonious. And some nice properties of sub-separation axioms are proved. For example, they are hereditary and product invariant, ＂L-good extension＂ in Lowen＇s sense, and the convergent of molecular nets is sole under a certain condition for the sub-T2 space. In addition, the relation between the sub-separation axioms defined in the paper and other separation axioms is also discussed.