{"title":"某些伪图空间的Baire性质","authors":"Katsuhisa Koshino","doi":"10.21099/TKBJM/1438951816","DOIUrl":null,"url":null,"abstract":"Let X be a compact metrizable space and Y be a nondegenerate dendrite with an end point 0. For each continuous function f : X ! Y , we define the hypo-graph # f 1⁄4 6 x AX fxg 1⁄20; f ðxÞ of f , where 1⁄20; f ðxÞ is the unique path from 0 to f ðxÞ in Y . Then we can regard #CðX ;Y Þ 1⁄4 f# f j f : X ! Y is continuousg as a subspace of the hyperspace consisting of non-empty closed sets in X Y equipped with the Vietoris topology. In this paper, we prove that #CðX ;Y Þ is a Baire space if and only if the set of isolated points of X is dense.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Baire property of certain hypo-graph spaces\",\"authors\":\"Katsuhisa Koshino\",\"doi\":\"10.21099/TKBJM/1438951816\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let X be a compact metrizable space and Y be a nondegenerate dendrite with an end point 0. For each continuous function f : X ! Y , we define the hypo-graph # f 1⁄4 6 x AX fxg 1⁄20; f ðxÞ of f , where 1⁄20; f ðxÞ is the unique path from 0 to f ðxÞ in Y . Then we can regard #CðX ;Y Þ 1⁄4 f# f j f : X ! Y is continuousg as a subspace of the hyperspace consisting of non-empty closed sets in X Y equipped with the Vietoris topology. In this paper, we prove that #CðX ;Y Þ is a Baire space if and only if the set of isolated points of X is dense.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2015-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/TKBJM/1438951816\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/1438951816","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
摘要
设X是一个紧化的可度量空间，Y是一个端点为0的非简并枝晶。对于每一个连续函数f: X !Y，我们定义伪图# f 1 / 4 6 x x x xg 1 / 20;F ðxÞ (F)其中1 / 20;f ðxÞ是Y中从0到f ðxÞ的唯一路径。那么我们可以考虑# c & X;Y Þ 1⁄4 f# f j f: X !Y作为具有Vietoris拓扑的由X Y中的非空闭集组成的超空间的子空间是连续的。本文证明了# c & X;Y Þ是一个Baire空间，当且仅当X的孤立点集是稠密的。
Let X be a compact metrizable space and Y be a nondegenerate dendrite with an end point 0. For each continuous function f : X ! Y , we define the hypo-graph # f 1⁄4 6 x AX fxg 1⁄20; f ðxÞ of f , where 1⁄20; f ðxÞ is the unique path from 0 to f ðxÞ in Y . Then we can regard #CðX ;Y Þ 1⁄4 f# f j f : X ! Y is continuousg as a subspace of the hyperspace consisting of non-empty closed sets in X Y equipped with the Vietoris topology. In this paper, we prove that #CðX ;Y Þ is a Baire space if and only if the set of isolated points of X is dense.
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