具有代数结构的拓扑空间（英文）

On Topological Spaces With Algebraic Structures

本文证明了:如果rectifiable空间G是局部Lindel?fΣ-空间,则G是强仿紧空间,该结论改进了文[Topology Appl.,2015,193:182-191]的一个结果;如果rectifiable空间G的某个紧化剩余是局部σ-空间,则G是局部紧空间或可分的度量空间,该结论推广了文[Topology Appl.,2010,157(4):789-799]的一个结果;如果非局部紧k-gentle仿拓扑群G在某个紧化bG中的剩余具有局部G_(δ-)对角线,则G是σ-紧的cosmic空间或者bG是可分的度量空间,该结论改进了文[Topology Appl.,2007,154(6):1084-1088]与[Topotogy Apt.,2009,156(5):849-854]的两个结果.

In this paper, we show that if a rectifiable space G is a locally Lindel6f ∑-space, then G is strongly paracompact, which improves a result given by Lin-Zhang-Zhang [Topology Appl., 2015, 193： 182-191]. We prove that if a rectifiable space G has a compactification bG such that bG ／ G is a locally a-space, then G is either locally compact or separable and metrizable, which generalizes a result obtained by Arhangel＇skii-Choban [Topology Appl., 2010, 157（4）： 789-799]. We also show that if a non-locMly compact k-gentle paratopological group G has a compactification bG such that bG ／ G has locally a Gδ-diagonal, then either G is a σ- compact cosmic space, or bG is separable and metrizable, which generalizes two results given by Arhangel＇skii [Topology Appl., 2007, 154（6）： 1084-1088] and Liu [Topology Appl., 2009, 156（5）： 849-854].