[分析] 請問1/f連續？(topo. or norm linear?)

看板Math作者Scape (non)時間10年前 (2014/06/22 08:36)推噓2(2推 0噓 2→)

留言4則, 2人參與討論串1/2 (看更多)

有個問題如下： f is a (real or complex) continuous function on X, f is not identically zero, i.e. Y = {x:f(x)≠0} is nonempty. Prove 1/f defined by (1/f)(x) = 1/f(x) is continuous at every point of Y. 我的問題是這裡的X，必須要是normed linear space嗎？或只是topological scape就可以？能否給個簡略的證明讓我看一下太久沒碰分析，卡關了...求救呀... -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 36.224.225.212 ※ 文章網址: http://www.ptt.cc/bbs/Math/M.1403397419.A.AF8.html

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yusd24

06/22 09:57, , 1^F

06/22 09:57, 1^F

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yusd24

06/22 09:59, , 2^F

06/22 09:59, 2^F

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Scape

06/22 12:07, , 3^F

06/22 12:07, 3^F