拓扑逆半群的一些基本性质

讨论拓扑逆半群的一些基本性质. 证明了拓扑逆半群的直积(和)仍是拓扑逆半群， 给出拓扑逆半群的半直积仍是拓扑逆半群的一些充分条件.此外， 还证明了在紧致拓扑逆半群中， 一个逆子半群的闭包是拓扑逆子半群， 一个Clifford子半群的闭包是Clifford拓扑逆子半群. 推广了已有拓扑半群或者拓扑群的一些结果.

Some fundamental properties of topological inverse semigroups

Some fundamental properties of topological inverse semigroups are discussed and it has been proved that the direct product/sum of a family of inverse semigroups is still an inverse semigroup and the semidirect product of two inverse semigroups is still an inverse semigroup under some certain conditions. In addition, it has been shown that in a given compact inverse semigroup, the closure of an inverse subsemigroup is a topological inverse subsemigroup, and the closure of a Clifford subsemigroup is a Clifford topological inverse subsemigroup. Thus the corresponding results related to topological semigroups or topological groups have been generalized.