{"title":"An explicit answer","authors":"W. Barit","doi":"10.1016/0016-660X(78)90009-0","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90009-0","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"49 1","pages":"297-298"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81381258","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}
{"title":"Products of topological spaces","authors":"J. E. Vaughan","doi":"10.1016/0016-660X(78)90001-6","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90001-6","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"44 1","pages":"207-217"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86435686","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}
{"title":"On extending continuous functions into a metrizable AE","authors":"L. Sennott","doi":"10.1016/0016-660X(78)90002-8","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90002-8","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"13 1","pages":"219-228"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90516202","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}
{"title":"Spaces with σ-point finite bases","authors":"W.N. Hunsaker, W.F. Lindgren","doi":"10.1016/0016-660X(78)90003-X","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90003-X","url":null,"abstract":"<div><p><em>Theorem</em>. Let <em>X</em> be a T<sub>1</sub> space. The following are equivalent:</p><ul><li><span>(1)</span><span><p><em>X</em> has a σ-disjoint base.</p></span></li><li><span>(FX2)</span><span><p><em>X</em> is quasi-developable and has a base that is the union of a sequence of rank 1 collections.</p></span></li><li><span>(3)</span><span><p><em>X</em> has a quasi-development (<span><math><mtext>G</mtext></math></span><sub>n</sub>) with the property that for each <em>x</em>, <span><math><mtext>{st</mtext><msup><mi></mi><mn>2</mn></msup><mtext>(x,</mtext><mtext>G</mtext><msub><mi></mi><mn>n</mn></msub><mtext>): x ∈st</mtext><msup><mi></mi><mn>2</mn></msup><mtext>(x,</mtext><mtext>G</mtext><msub><mi></mi><mn>n</mn></msub><mtext>)</mtext></math></span>, <em>n</em> a positive integer} is a base for <span><math><mtext>N</mtext></math></span> (x).</p></span></li></ul><p><em>Theorem</em>. Let <em>X</em> be a T<sub>1</sub> space. The following are equivalent:</p><ul><li><span>(1)</span><span><p><em>X</em> has a <em>σ</em>-point finite base.</p></span></li><li><span>(2)</span><span><p><em>X</em> has a quasi-development (<span><math><mtext>G</mtext></math></span><sub><em>n</em></sub>) with each <span><math><mtext>G</mtext></math></span><sub><em>n</em></sub> well ranked.</p></span></li><li><span>(3)</span><span><p><em>X</em> has a quasi-development (<span><math><mtext>G</mtext></math></span><sub><em>n</em></sub>) with each <span><math><mtext>G</mtext></math></span><sub><em>n</em></sub> Noetherian of sub-infinite rank.</p></span></li><li><span>(4)</span><span><p><em>X</em> has a quasi-development (<span><math><mtext>G</mtext></math></span><sub><em>n</em></sub>) with each <span><math><mtext>G</mtext></math></span><sub><em>n</em></sub> Noetherian of point finite rank.</p></span></li></ul></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 229-232"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90003-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91688460","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}
{"title":"The category of all zero-dimensional realcompact spaces is not simple","authors":"A. Mysior","doi":"10.1016/0016-660X(78)90005-3","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90005-3","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"1 1","pages":"259-264"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88771693","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}
{"title":"On shape of product spaces","authors":"Yukihiro Kodama","doi":"10.1016/0016-660X(78)90045-4","DOIUrl":"10.1016/0016-660X(78)90045-4","url":null,"abstract":"<div><p>It is known that if <em>X</em> is a compactum and <em>Y</em> is metrizable Sh<sub>5</sub>(<em>X</em> × <em>Y</em>) is not generally determined by Sh<sub>5</sub>(<em>X</em>) and Sh<sub>5</sub>(<em>Y</em>), where Sh<sub>5</sub>(<em>Z</em>) is the strong shape of <em>Z</em> in the sense of Borsuk. In this paper it is proved that Sh(<em>X</em> × <em>Y</em>) is uniquely determined by Sh(<em>X</em>) and Sh(<em>Y</em>), where Sh(<em>Z</em>) is the shape of <em>Z</em> in the sense of Fox. If <em>X</em> is an FANR and <em>Y</em> is an MANR, then <em>X</em> × <em>Y</em> is an MANR.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 141-150"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90045-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81260118","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}
{"title":"On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps","authors":"Peter I. Booth, Ronald Brown","doi":"10.1016/0016-660X(78)90048-X","DOIUrl":"10.1016/0016-660X(78)90048-X","url":null,"abstract":"<div><p>A previous paper constructed exponential laws in the category <strong>Top<sub><em>B</em></sub></strong> of spaces over <em>B</em>. The present paper relates these laws to constructions known for locally trivial maps, and constructs also new exponential laws for ex-spaces, fibred section spaces and fibred relative lifting spaces. Versions of these laws for homotopy classes of maps are discussed.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 165-179"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90048-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86287533","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}
{"title":"On linear topologies determined by a family of subsets of a topological vector space","authors":"Peter Dierolf, Susanne Dierolf","doi":"10.1016/0016-660X(78)90044-2","DOIUrl":"10.1016/0016-660X(78)90044-2","url":null,"abstract":"<div><p>We provide a general framework for the study of the finest linear (locally convex) topology which coincides on a family of subsets with a given linear (locally convex) topology. It is proved that the formation of such topologies always commutes with linear direct sums. We characterize the corresponding situation for products and prove a result about locally convex direct sums sufficiently general to cover the examples which already occurred in the literature. Moreover the 0-nbhd. filters of such topologies are characterized, and several examples are considered.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 127-140"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90044-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73574081","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}
{"title":"Not all compact Hausdorff spaces are supercompact","authors":"Murray G. Bell","doi":"10.1016/0016-660X(78)90046-6","DOIUrl":"10.1016/0016-660X(78)90046-6","url":null,"abstract":"<div><p>De Groot and Verbeek have both asked for an example of a compact Hausdorff space which is not supercompact. Is is shown here that if <em>X</em> is not pseudocompact, then β<em>X</em> is not supercompact. It is done in the more general setting of Wallman compactifications.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 151-155"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90046-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81368203","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}
{"title":"Topological properties in nearness spaces","authors":"John W. Carlson","doi":"10.1016/0016-660X(78)90042-9","DOIUrl":"10.1016/0016-660X(78)90042-9","url":null,"abstract":"<div><p>Characterization of countably compact, Lindelof, <em>H</em>-closed, first countable and second countable are provided in terms of the nearness structure. Applications of these results are provided for uniform spaces and specific nearness structures.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 111-118"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90042-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89249953","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
