﻿ 一类新型半拓扑空间及其分离性质

# 一类新型半拓扑空间及其分离性质A New Semi-Topological Space and Its Separation Property

2002年，A. Csaszar引入的广义拓扑空间定义仅包含拓扑空间定义条件的一半。因此，广义拓扑实际上是一类半拓扑。如果把广义拓扑相对于拓扑的另一半条件作为另一类半拓扑，那么这类半拓扑能否像广义拓扑那样具有一些良好的特征性质？本文就此问题进行研究，在这类半拓扑的点集理论和分离性质获得了一系列结果。

Abstract: In 2002, the concept of a generalized topological space was introduced by A. Csaszar. But it contains only half of the conditions in the definition of a topological space. Therefore, a generalized topology is a kind of semi-topologies actually. If we use the other condition of a topology which is contrary to the generalized topology as another semi-topology, can this new semi-topology be of some good properties, just like a generalized topology? This thesis is about this problem, and several results are obtained for the theories of point set and separation properties of this semi-topological space.

[1] Csaszar, A. (2005) Generalized open sets in generalized topologies. Acta Mathematica Hungarica, 106, 53-66. http://dx.doi.org/10.1007/s10474-005-0005-5

[2] Min, W.K. (2009) Weak continuity on generalized topological spaces. Acta Mathematica Hungarica, 124, 73-81. http://dx.doi.org/10.1007/s10474-008-8152-0

[3] Min, W.K. (2009) Almost continuity on generalized topological spaces. Acta Mathematica Hungarica, 125, 121-125. http://dx.doi.org/10.1007/s10474-009-8230-y

[4] Csaszar, A. (2008) On generalized neighbourhood systems. Acta Mathematica Hungarica, 121, 395-400. http://dx.doi.org/10.1007/s10474-008-7224-5

[5] Sarma, R.D. (2010) On convergence in generalized topology. In-ternational Journal of Pure and Applied Mathematics, 60, 51-56.

[6] Sarm, R.D. (2012) On extremely disconnected generalized topologies. Acta Mathematica Hungarica, 134, 583-588. http://dx.doi.org/10.1007/s10474-011-0153-8

[7] Wu, X. and Zhu, P. (2013) A note on β-connectedness. Acta Ma-thematica Hungarica, 139, 252-254. http://dx.doi.org/10.1007/s10474-012-0276-6

[8] Csaszar, A. (2002) Generalized topology, generalized continuity. Acta Mathematica Hungarica, 96, 351-357. http://dx.doi.org/10.1023/A:1019713018007

[9] 朱培勇, 雷银彬 (2009) 拓扑学导论. 科学出版社, 北京.

[10] 熊金城 (2011) 点集拓扑讲义. 第四版, 高等教育出版社, 北京.

Top