{"title":"Δ-Maximal topologies for some cardinal functions","authors":"Douglas E. Cameron","doi":"10.1016/0016-660X(78)90051-X","DOIUrl":"10.1016/0016-660X(78)90051-X","url":null,"abstract":"<div><p>In this paper we introduce the concept of Δ-maximal topologies and characterize Δ-maximal topological spaces for a class of topological properties which include the cardinal functions κ-dense, Sanin, Caliber-κ, and the countable chain condition. In addition special consideration is given to the existence of Δ-maximal κ-dense spaces which are finer than a given κ-dense topology and also investigated are the existence of Δ-maximal second countable spaces.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 59-70"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90051-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79587944","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":"A near-selection theorem","authors":"William E. Haver","doi":"10.1016/0016-660X(78)90056-9","DOIUrl":"10.1016/0016-660X(78)90056-9","url":null,"abstract":"<div><p>A near-selection theorem is proven for carriers defined on spaces that are the countable union of finite dimensional compacta. As an application a new proof is given of the fact that the space of homeomorphisms on a compact piecewise linear manifold is locally contractible. In addition a new criterion is given to determine if the space of homeomorphisms on a compact <em>n</em>-manifold is an <em>l</em><sub>2</sub>-manifold.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 117-124"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90056-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80014550","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":"Nearnesses of finite order and uniqueness conditions for associated compactifications","authors":"A.J. Ward","doi":"10.1016/0016-660X(78)90053-3","DOIUrl":"10.1016/0016-660X(78)90053-3","url":null,"abstract":"<div><p>Nearnesses of finite order are defined, and in particular a sub-class (called Ivanov <em>n</em>-nearnesses) which includes the class of Lodato proximities and leads to contiguities as a limiting case. A canonical compactification by maximal clans is constructed and characterised descriptively, thus unifying the compactification theories of I.O-proximities and of contiguities. Finally, it is shown how all maximal clans with respect to the finest contiguity compatible with a given Ivanov <em>n</em>-nearness can be constructed from prime closed filters, using not more than <em>n</em> such filters for each clan.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 89-99"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90053-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89751219","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":"θ-spaces","authors":"Peter Fletcher, William F. Lindgren","doi":"10.1016/0016-660X(78)90059-4","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90059-4","url":null,"abstract":"<div><p>This paper studies the relationships of θ-spaces to other generalized metric spaces. In particular, a condition shared by θ-spaces and spaces with a quasi-<em>G<sub>g</sub></em> diagonal is introduced, and it is shown that every regular θ refinable β-space satisfying this condition is semi-stratifiable. In addition, a regular quasi-complete space satisfying this condition has a base of countable order.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 139-153"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90059-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137284260","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 epimorphisms of topological groups","authors":"Eric C. Nummela","doi":"10.1016/0016-660X(78)90060-0","DOIUrl":"10.1016/0016-660X(78)90060-0","url":null,"abstract":"<div><p>A complete survey of results on the epimorphism problem for various categories of topological groups is given. All known partial results on the epimorphism problem for Hausdorff topological groups support the conjecture that epimorphisms of Hausdorff topological groups have dense image.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 155-167"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90060-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85154250","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 Bing staircase construction for Hilbert cube manifolds","authors":"M. Handel","doi":"10.1016/0016-660X(78)90040-5","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90040-5","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"31 1","pages":"29-40"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80348002","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":"Lattices of compactifications of Tychonoff spaces","authors":"Y. Ünlü","doi":"10.1016/0016-660X(78)90041-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90041-7","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"18 1","pages":"41-57"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74930421","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 certain sums of Hilbert cubes","authors":"M. Handel","doi":"10.1016/0016-660X(78)90039-9","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90039-9","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"88 1","pages":"19-28"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76407019","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 certain sums of Hilbert cubes","authors":"Michael Handel","doi":"10.1016/0016-660X(78)90039-9","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90039-9","url":null,"abstract":"<div><p>Sufficient conditions are given for the union of two Hilbert cube (manifolds) intersecting in a Hilbert cube (manifold) to be a Hilbert cube (manifold). The corollaries include a non-stabilized mapping cylinder theorem for embeddings between Hilbert cube manifolds and a sum theorem for Keller cubes.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 19-28"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90039-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90123071","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":"Shape properties of the Stone-Čech compactification","authors":"James Keesling, R.B. Sher","doi":"10.1016/0016-660X(78)90037-5","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90037-5","url":null,"abstract":"<div><p>In this paper it is shown that if <em>X</em> is a connected space which is not pesudocompact, then β<em>X</em> is not movable and does not have metric shape. In particular β<em>X</em> cannot have trivial shape. It is also shown that if <em>X</em> is Lindelöf and <em>KχβX</em>−<em>X</em> is a continuum, then <em>K</em> cannot be movable or have metric shape unless it is a point.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 1-8"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90037-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91696601","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}
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