关于空间和映射Ⅱ
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摘要
在文章《关于空间和映射》的基础上,描述在拓扑空间的研究中具有一定作用的30个拓扑空间类在商映射,闭映射,具有Lindel■f纤维的闭映射,完备映射,有限到一闭映射,开映射,开紧映射和有限到一开映射作用下的不变性和逆不变性.
Based on the article "On spaces and mappings", a survey is given on invariants and inverse invariants of thirty topological space classes which play a certain role in the study of the theory of topological spaces under quotient mappings, closed mappings, closed mappings with Lindel■f fibers, perfect mappings,finite-to-one closed mappings, open mappings, open-compact mappings and finite-to-one open mappings.
Based on the article "On spaces and mappings", a survey is given on invariants and inverse invariants of thirty topological space classes which play a certain role in the study of the theory of topological spaces under quotient mappings, closed mappings, closed mappings with Lindel■f fibers, perfect mappings,finite-to-one closed mappings, open mappings, open-compact mappings and finite-to-one open mappings.
引文
[1]LIN S,YUN Z.Generalized metric spaces and mappings[M].Beijing:Science Press,2017.
[2]林寿.《空间与映射》50年[J].四川师范大学学报(自然科学版),2017,40(1):133-142.
[3]林寿.关于Arhangel’skiǐ的“映射与空间”[J].苏州大学学报(自然科学版),1992,8(4):393-400.
[4]林寿.关于空间和映射[J].苏州大学学报(自然科学版),1989,5(3):313-326.
[5]GITTINGS R F.Open mapping theory[C]//REED G M.Set-theoretic Topology(Paper,Inst Medicine and Math,Ohio Univ,Athens,1975-1976)New York:Academic Press,1977:141-191.
[6]杨洁.有限到一闭映射[J].闽南师范大学学报(自然科学版),2017,30(2):1-7.
[7]林寿.点可数覆盖与序列覆盖映射[M].2版.北京:科学出版社,2015.
[8]杨洁.关于空间与映射的注记[J].广西师范学院学报(自然科学版),2018,35(1):17-20.
[9]GE X.On so-metrizable spaces[J].Mat Vesnik,2009,61(3):209-218.
[10]葛英.关于sn度量空间[J].数学学报,2002,45(2):355-360.
[11]BANAKH T,BAGACHEV V,KOLESNIKOV A.k*-Metrizable spaces and their applications[J].J Math Sci,2008,155(4):475-522.
[12]LIU C,TANAKA Y.Spaces havingσ-compact-finite k-networks and related matters[J].Topology Proc,1996,21:173-200
[13]SAKAI M.Remarks on spaces with special type of k-networks[J].Tsukuba J Math,1997,21:443-448.
[14]沈荣鑫.弱拟第一可数空间与映射[J].四川大学学报(自然科学版),2010,47(4):693-696.
[15]YANG J,LIN S.The closed finite-to-one mappings and their applications[J].Applied Mathematics:a Journal of Chinese Universities,2019,34.
[16]TANG Z,LIN S,LIN F.Symmetric products and closed finite-to-one mappings[J].Topology Appl,2018,234:26-45.
[17]林寿.关于开紧映射与Arhangel’skiǐ的问题[J].数学年刊,2006,27:719-722.
[18]VAUGHAN J E.Spaces of countable and point-countable type[J].Trans Amer Math Soc,1970,151:341-351.
[19]MICHAEL E.On k-spaces,kR-spaces and k(X)[J].Pacific J Math,1973,47(2):487-498.
[20]MOU L,OHTA H.Sharp bases and mappings[J].Houston J Math.2005,31(1):227-237.
[21]SHIBAKOV A.On spaces with point-countable k-networks and their mappings[J].Serdica-Bulgaricae Math Pah,1994,20(1):48-55.
[22]高国士.拓扑空间论[M].2版.北京:科学出版社,2008.
[23]CHEN H,LIN S.A note on spaces with regular Gδ-diagonals[J].J Math Research Exposition,1999,19(3):546-548.
[24]POPOV V.A perfect map need not preserve a Gδ-diagonal[J].Gen Top Appl,1997,7:31-33.
[25]XIA S.Mappings theorems on some generalized metric spaces[J].Q and A in General Topology,1988,6:107-115.
[26]林寿.关于Σ*空间[J].辽宁师范大学学报(自然科学版),1991,14(3):177-180,184.
[27]CHABER J.More nondevelopable spaces in MOBI[J].Proc Amer Math Soc,1988,103:307-313.
[28]林寿.度量空间与函数空间的拓扑[M].北京:科学出版社,2004.
[29]刘川.关于点可数覆盖[J].数学研究与评论,1996,16(1):121-124.
[30]林寿,葛英.csf可数空间的注记[J].高校应用数学学报,2017,32(1):79-86.
[31]SHEN R.On generalized metrizable properties in quasitopological groups[J].Topology Appl,2014,173(3):219-226.
[2]林寿.《空间与映射》50年[J].四川师范大学学报(自然科学版),2017,40(1):133-142.
[3]林寿.关于Arhangel’skiǐ的“映射与空间”[J].苏州大学学报(自然科学版),1992,8(4):393-400.
[4]林寿.关于空间和映射[J].苏州大学学报(自然科学版),1989,5(3):313-326.
[5]GITTINGS R F.Open mapping theory[C]//REED G M.Set-theoretic Topology(Paper,Inst Medicine and Math,Ohio Univ,Athens,1975-1976)New York:Academic Press,1977:141-191.
[6]杨洁.有限到一闭映射[J].闽南师范大学学报(自然科学版),2017,30(2):1-7.
[7]林寿.点可数覆盖与序列覆盖映射[M].2版.北京:科学出版社,2015.
[8]杨洁.关于空间与映射的注记[J].广西师范学院学报(自然科学版),2018,35(1):17-20.
[9]GE X.On so-metrizable spaces[J].Mat Vesnik,2009,61(3):209-218.
[10]葛英.关于sn度量空间[J].数学学报,2002,45(2):355-360.
[11]BANAKH T,BAGACHEV V,KOLESNIKOV A.k*-Metrizable spaces and their applications[J].J Math Sci,2008,155(4):475-522.
[12]LIU C,TANAKA Y.Spaces havingσ-compact-finite k-networks and related matters[J].Topology Proc,1996,21:173-200
[13]SAKAI M.Remarks on spaces with special type of k-networks[J].Tsukuba J Math,1997,21:443-448.
[14]沈荣鑫.弱拟第一可数空间与映射[J].四川大学学报(自然科学版),2010,47(4):693-696.
[15]YANG J,LIN S.The closed finite-to-one mappings and their applications[J].Applied Mathematics:a Journal of Chinese Universities,2019,34.
[16]TANG Z,LIN S,LIN F.Symmetric products and closed finite-to-one mappings[J].Topology Appl,2018,234:26-45.
[17]林寿.关于开紧映射与Arhangel’skiǐ的问题[J].数学年刊,2006,27:719-722.
[18]VAUGHAN J E.Spaces of countable and point-countable type[J].Trans Amer Math Soc,1970,151:341-351.
[19]MICHAEL E.On k-spaces,kR-spaces and k(X)[J].Pacific J Math,1973,47(2):487-498.
[20]MOU L,OHTA H.Sharp bases and mappings[J].Houston J Math.2005,31(1):227-237.
[21]SHIBAKOV A.On spaces with point-countable k-networks and their mappings[J].Serdica-Bulgaricae Math Pah,1994,20(1):48-55.
[22]高国士.拓扑空间论[M].2版.北京:科学出版社,2008.
[23]CHEN H,LIN S.A note on spaces with regular Gδ-diagonals[J].J Math Research Exposition,1999,19(3):546-548.
[24]POPOV V.A perfect map need not preserve a Gδ-diagonal[J].Gen Top Appl,1997,7:31-33.
[25]XIA S.Mappings theorems on some generalized metric spaces[J].Q and A in General Topology,1988,6:107-115.
[26]林寿.关于Σ*空间[J].辽宁师范大学学报(自然科学版),1991,14(3):177-180,184.
[27]CHABER J.More nondevelopable spaces in MOBI[J].Proc Amer Math Soc,1988,103:307-313.
[28]林寿.度量空间与函数空间的拓扑[M].北京:科学出版社,2004.
[29]刘川.关于点可数覆盖[J].数学研究与评论,1996,16(1):121-124.
[30]林寿,葛英.csf可数空间的注记[J].高校应用数学学报,2017,32(1):79-86.
[31]SHEN R.On generalized metrizable properties in quasitopological groups[J].Topology Appl,2014,173(3):219-226.