﻿ 关于L-半拓扑空间的一些注记

# 关于L-半拓扑空间的一些注记Some Notes on L-Semi Topological Space

Abstract: 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.

[1] Csaszar, A. (2002) Generalized Topology, Generalized Continuity. Acta Mathematica Hungarica, 96, 351-357.
http://dx.doi.org/10.1023/A:1019713018007

[2] Csaszar, A. (2005) Generalized Open Sets in Generalized To-pologies. Acta Mathematica Hungarica, 106, 53-66.
http://dx.doi.org/10.1007/s10474-005-0005-5

[3] Csaszar, A. (1997) Generalized Open Sets. Acta Mathematica Hungarica, 75, 65-87.
http://dx.doi.org/10.1023/A:1006582718102

[4] Csaszar, A. (2009) Products of Generalized Topologies. Acta Mathematica Hungarica, 123, 127-132.
http://dx.doi.org/10.1007/s10474-008-8074-x

[5] Csaszar, A. (2004) Separation Axioms for Generalized To-pologies. Acta Mathematica Hungarica, 104, 63-69.

[6] Min, W.K. (2010) Remarks on Separation Axioms on Gene-ralized Topological Space. Chungcheong Mathematical Society, 23, 293-298.

[7] Sarsak, M.S. (2011) Weak Separa-tion Axioms in Generalized Topological Spaces. Acta Mathematica Hungarica, 131, 110-121.
http://dx.doi.org/10.1007/s10474-010-0017-7

[8] Shen, R. (2009) Remarks on Products of Generalized Topolo-gies. Acta Mathematica Hungarica, 124, 363-369.
http://dx.doi.org/10.1007/s10474-009-8207-x

[9] 胡西超, 朱培勇. 一类新型半拓扑空间及其分离性质[J]. 理论数学, 2015, 5(4): 129-135.

[10] 朱培勇, 雷银彬. 拓扑学导论[M]. 北京: 科学出版社, 2009: 44-50.

Top