{"title":"Shape properties of the Stone-Čech compactification","authors":"J. Keesling, R. Sher","doi":"10.1016/0016-660X(78)90037-5","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90037-5","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"154 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79722361","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":"L-spaces in complete spaces of countable tightness using ♢","authors":"J. Ginsburg","doi":"10.1016/0016-660X(78)90038-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90038-7","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"2010 14","pages":"9-17"},"PeriodicalIF":0.0,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91429409","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":"Yusuf Ünlü","doi":"10.1016/0016-660X(78)90041-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90041-7","url":null,"abstract":"<div><p>It is shown that, for a Tychonoff space <em>X</em>, the complete upper semilattice <em>K</em>(<em>X</em>) of compactifications of <em>X</em> is a lattice if either (1) β<em>X</em>⧹<em>X</em> is realcompact and <em>C<sup>∗</sup></em>-embedded in β<em>X</em>, or (2) β<em>X</em>⧹<em>X</em> is a <em>P</em>-space and cl<sub>β<em>X</em></sub>(β<em>X</em>⧹<em>X</em>) is an <em>F</em>-space. The concept of bounding lattice is introduced and examples of spaces <em>X</em> are given such that <em>K</em>(<em>X</em>) is a lattice but not a bounding lattice. A certain class of Tychonoff spaces <em>X</em> is constructed such that <em>K</em>(<em>X</em>) is a lattice.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 41-57"},"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)90041-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91696598","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":"L-spaces in complete spaces of countable tightness using ♢","authors":"John Ginsburg","doi":"10.1016/0016-660X(78)90038-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90038-7","url":null,"abstract":"<div><p>The set theoretic principle ♢ is used to construct hereditarily Lindelof, non-separable subspaces of given complete spaces of countable tightness. The construction is patterned after R. B. Jensen's original use of ♢ to construct a Souslin line, and yields the following result: Suppose <em>X</em> is a regular space of countable tightness having weight at most <em>c</em>. If no non-empty <em>G</em><sub>δ</sub> set in <em>X</em> is contained in a separable subspace of <em>X</em>, and if either <em>X</em> is countably complete or has all closed subsets Baire, then <em>X</em> contains an L-space.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 9-17"},"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)90038-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91696600","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":"Michael Handel","doi":"10.1016/0016-660X(78)90040-5","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90040-5","url":null,"abstract":"<div><p>Finite dimensional techniques of Bing and Bryant are extended to Hilbert cube manifolds to show that <span><math><mtext>M</mtext><mtext>A</mtext><mtext> × Q = M</mtext></math></span> where <em>M</em> is a Hilbert cube manifold, <em>A</em> is an embedded copy of <em>1</em><sup>k</sup>, 0<span><math><mtext></mtext><mtext>̌</mtext></math></span>k<span><math><mtext></mtext><mtext>̌</mtext></math></span>∞, and <em>Q</em> is the Hilbert cube. Among the corollaries given here are elementary proofs of two theorems of West: the mapping cylinder theorem and the sum theorem for Hilbert cube factors.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 29-40"},"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)90040-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91696599","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":"Scattered spaces and their compactifications","authors":"R.C. Solomon","doi":"10.1016/0016-660X(78)90010-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90010-7","url":null,"abstract":"<div><p>We show that a known restriction on the cardinalities of closures of subspaces of scattered We then find a wide class of spaces, <span><math><mtext>∥</mtext><mtext>A</mtext><mtext>̄</mtext><mtext>∥ ⩽ 2</mtext><msup><mi></mi><mn>∥A∥</mn></msup></math></span>, cannot be improved to <span><math><mtext>∥</mtext><mtext>A</mtext><mtext>̄</mtext><mtext>∥ ⩽ ∥A∥ </mtext><msup><mi></mi><mn>λ</mn></msup></math></span>, for any λ.T.3<span><math><mtext>1</mtext><mtext>2</mtext></math></span>. scattered spaces which have no scattered compactification: these spaces are derived from regular filters over cardinals bigger than <strong>N</strong><sub>1</sub>.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 299-301"},"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)90010-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91635787","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 extending continuous functions into a metrizable AE","authors":"L.I. Sennott","doi":"10.1016/0016-660X(78)90002-8","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90002-8","url":null,"abstract":"<div><p>We say that a subset <em>S</em> of a topological space <em>X</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>0</sub></em></sup>-embedded) in <em>X</em> if every map from <em>S</em> to a (separable) metrizable AE can be extended over <em>X</em>. Characterizations of <em>M</em>-and <em>M<em><sup>N<sub>O</sub></sup></em></em>-embedding are given and we prove that <em>S</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>O</sub></em></sup>-embedded) in <em>X</em> iff(<em>X,S</em>) has the Homotopy Extension Property with respect to every (seperable) ANR space.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 219-228"},"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)90002-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91635762","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":"Basis properties of topologies compatible with (not necessarily symmetric) distance-functions","authors":"H. Reichel","doi":"10.1016/0016-660X(78)90007-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90007-7","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"62 1","pages":"283-289"},"PeriodicalIF":0.0,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77912271","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":"Basis properties of topologies compatible with (not necessarily symmetric) distance-functions","authors":"Hans-Christian Reichel","doi":"10.1016/0016-660X(78)90007-7","DOIUrl":"https://doi.org/10.1016/0016-660X(78)90007-7","url":null,"abstract":"<div><p>One of the aims of this paper is to generalize a theorem of P. Fletcher and W.F. Lindgren characterizing second countable spaces. On behalf of that, we investigate a basis property related to the concept of σ-<em>Q</em>-bases defined by Fletcher and Lindgren and orthobases studied by P. Nyikos and W.F. Lindgren. In this new setting we state a necessary and sufficient condition for ω<sub>μ</sub>-quasimetrizability of topological spaces and we discuss a problem of P. Fletcher and W.F. Lindgren and a related theorem of S. Nedev concerning quasimetrizability of <em>T</em><sub>1</sub>-spaces. As a corollary we give a characterization of ω<sub>μ</sub>-additive spaces having a base of cardinality ω<sub>μ</sub>— In the second part of the paper, we study (not necessarily symmetric) distance-functions on a space <em>X</em> taking their values in a partially ordered group <em>H</em>. We show that every <em>T</em><sub>1</sub>-space <em>X</em> is quasimetrizable in this generalized sense.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 283-289"},"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)90007-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91635764","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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