[分析] 有關topological vector space

看板Math作者 (請拒絕看各新聞台)時間9年前 (2016/10/09 16:09), 編輯推噓0(0推 0噓 5→)
留言5則, 2人參與, 最新討論串1/1
大家好 小弟唸到topological vector space發現其很難想像 需要一點指點 Let V be a topological vector space(not necessarily Hausdorff). Let W be a subspace of V (with E in W being open if and only if E being an intersection of W and some open set in V). Question 1: Is W a topological vector space? Question 2: If the answer to question 1 is negative, please give me a counterexample. What if W being finite-dimensional? 謝謝大家 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.128.67.243 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1476000583.A.75D.html
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10/09 17:34, , 1F
which category is W a subspce of V? TS/VS/TVS?
10/09 17:34, 1F
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10/10 00:27, , 2F
W是V的 vector subspace, 若照topological subspace
10/10 00:27, 2F
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10/10 00:27, , 3F
的方式定義W的topology, 問此topology是否會使W 成
10/10 00:27, 3F
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10/10 00:27, , 4F
為TVS
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10/10 14:30, , 5F
(1) Yes, just look at subspace topology (2) N/A
10/10 14:30, 5F
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