{"title":"SC(X)=RX什么时候成立?","authors":"Bogdan Bokalo, Nadiya Kolos","doi":"10.1016/j.top.2009.11.016","DOIUrl":null,"url":null,"abstract":"<div><p>A map <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> between topological spaces is called scatteredly continuous if for each non-empty subspace <span><math><mi>A</mi><mo>⊂</mo><mi>X</mi></math></span> the restriction <span><math><mi>f</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>A</mi></mrow></msub></math></span> has a point of continuity. By <span><math><mi>S</mi><mi>C</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> we denote the set of all scatteredly continuous maps from <span><math><mi>X</mi></math></span> to the space of real numbers <span><math><mi>R</mi></math></span>. We consider the following problem: What conditions must satisfy space <span><math><mi>X</mi></math></span> so that <span><math><mi>S</mi><mi>C</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>X</mi></mrow></msup></math></span>?</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 178-181"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.016","citationCount":"2","resultStr":"{\"title\":\"When does SC(X)=RX hold?\",\"authors\":\"Bogdan Bokalo, Nadiya Kolos\",\"doi\":\"10.1016/j.top.2009.11.016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A map <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> between topological spaces is called scatteredly continuous if for each non-empty subspace <span><math><mi>A</mi><mo>⊂</mo><mi>X</mi></math></span> the restriction <span><math><mi>f</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>A</mi></mrow></msub></math></span> has a point of continuity. By <span><math><mi>S</mi><mi>C</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> we denote the set of all scatteredly continuous maps from <span><math><mi>X</mi></math></span> to the space of real numbers <span><math><mi>R</mi></math></span>. We consider the following problem: What conditions must satisfy space <span><math><mi>X</mi></math></span> so that <span><math><mi>S</mi><mi>C</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>X</mi></mrow></msup></math></span>?</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"48 2\",\"pages\":\"Pages 178-181\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2009.11.016\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938309000287\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938309000287","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A map between topological spaces is called scatteredly continuous if for each non-empty subspace the restriction has a point of continuity. By we denote the set of all scatteredly continuous maps from to the space of real numbers . We consider the following problem: What conditions must satisfy space so that ?
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