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A characterization of almost periodic homeomorphisms on the 2-sphere and the annulus 2球和环上概周期同胚的刻画
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90022-3
Gerhard X. Ritter
{"title":"A characterization of almost periodic homeomorphisms on the 2-sphere and the annulus","authors":"Gerhard X. Ritter","doi":"10.1016/0016-660X(78)90022-3","DOIUrl":"10.1016/0016-660X(78)90022-3","url":null,"abstract":"<div><p>The purpose of this paper is to show that every almost periodic homeomorphism of the 2-sphere or the annulus onto itself is topologically equivalent to either a standard rotation or a standard reflection or the composition of a standard reflection with a standard rotation of these spaces.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 185-191"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90022-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79890464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Shape fibrations I 形状振动I
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90023-5
S. Mardešić, T. Rushing
{"title":"Shape fibrations I","authors":"S. Mardešić, T. Rushing","doi":"10.1016/0016-660X(78)90023-5","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90023-5","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":" 3","pages":"193-215"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91514911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 44
Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants 对于序不变量和基数不变量，伪开函数是单调递减的
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90028-4
James R. Boone
{"title":"Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants","authors":"James R. Boone","doi":"10.1016/0016-660X(78)90028-4","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90028-4","url":null,"abstract":"<div><p>A new property of pseudo-open functions is presented in this paper. Pseudo-open functions are monotonic decreasing with respect to ordinal and cardinal invariants defined by compact and sequential closures. A weak form of continuity, called <em>k</em>-continuous, is defined, characterized and used in the proof of the monotonicity properties of pseudo-open mappings. The relationships between the classes of <em>k</em>-continuous and sequentially continuous mappings in the category of all topological spaces and the continuous mappings in the subcategories of <em>k</em>-spaces and sequential spaces are presented.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 243-251"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90028-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91638695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Gσ-sets in symmetrizable and related spaces 对称及相关空间中的g σ-集
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90029-6
S.W. Davis, G. Gruenhage, P.J. Nyikos
{"title":"Gσ-sets in symmetrizable and related spaces","authors":"S.W. Davis,&nbsp;G. Gruenhage,&nbsp;P.J. Nyikos","doi":"10.1016/0016-660X(78)90029-6","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90029-6","url":null,"abstract":"<div><p>In this paper we answer questions of Arhangel'skii and Michael by providing an example of a regular symmetrizable space which is not subparacompact and has a closed subset which is not a <em>G</em><sub>σ</sub>-set. We also use the idea of sequential order to obtain some positive results, and several examples are provided which show that these results are in some sense the best possible.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 253-261"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90029-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91638696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Contractibility of Whitney continua in C(X) C(X)中Whitney连续体的可缩性
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90031-4
Ann Petrus
{"title":"Contractibility of Whitney continua in C(X)","authors":"Ann Petrus","doi":"10.1016/0016-660X(78)90031-4","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90031-4","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"55 1","pages":"275-288"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87728925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 27
A note on a theorem of arhangel'skiǐ 关于arhangel' skiy的一个定理的注解
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90024-7
Mohammad Ismail
{"title":"A note on a theorem of arhangel'skiǐ","authors":"Mohammad Ismail","doi":"10.1016/0016-660X(78)90024-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90024-7","url":null,"abstract":"<div><p>Arhangel'skiǐ proved that the Continuum Hypothesis implies that if a regular space <em>X</em> is hereditarily of pointwise countable type then the set of points as which the character of <em>X</em> is countable is a dense subset of <em>X</em>. In this note we prove this theorem without the use of the Continuum Hypothesis.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 217-220"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90024-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90003230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants 对于序不变量和基数不变量，伪开函数是单调递减的
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90028-4
James R. Boone
{"title":"Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants","authors":"James R. Boone","doi":"10.1016/0016-660X(78)90028-4","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90028-4","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"39 7","pages":"243-251"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72588011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Gσ-sets in symmetrizable and related spaces 对称及相关空间中的g σ-集
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90029-6
S. W. Davis, G. Gruenhage, P. Nyikos
{"title":"Gσ-sets in symmetrizable and related spaces","authors":"S. W. Davis, G. Gruenhage, P. Nyikos","doi":"10.1016/0016-660X(78)90029-6","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90029-6","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"40 1","pages":"253-261"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89945810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Martin's axiom and normality 马丁公理和正态性
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90030-2
I. Juhász, W. Weiss
{"title":"Martin's axiom and normality","authors":"I. Juhász, W. Weiss","doi":"10.1016/0016-660X(78)90030-2","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90030-2","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"11 1","pages":"263-274"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78897284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Contractibility of Whitney continua in C(X) C(X)中Whitney连续体的可缩性
General Topology and its Applications Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90031-4
Ann Petrus
{"title":"Contractibility of Whitney continua in C(X)","authors":"Ann Petrus","doi":"10.1016/0016-660X(78)90031-4","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90031-4","url":null,"abstract":"<div><p>We show that there are Whitney maps on the 2-cell such that Whitney continua in the hyperspace of the 2-cell are non-contractible, non-locally contractible, and have non-trivial Čhech cohomology in dimension 2. This implies that contractibility, local contractibility, being an AR, being an ANR, and acyclicity in Čech cohomology are not Whitney properties. We show, however, that contractibility is a Whitney property for the class of dendrites.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 275-288"},"PeriodicalIF":0.0,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90031-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91639160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 27
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