Re: [微積] 函數的連續性

看板Math作者 (紳士的野蠻要藏在袖子裡)時間12年前 (2013/09/30 05:11), 編輯推噓0(0推 0噓 3→)
留言3則, 2人參與, 最新討論串2/2 (看更多)
f is continuous <=> preimage of an open set is open <=> preimage of a closed set is closed choose any subinterval J with irrational end points, then f^{-1}(J) is open and closed, so it is either empty or R. So obviously f is a constant. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.247.0.119 ※ 編輯: JASS0213 來自: 140.247.0.119 (09/30 05:13)
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09/30 11:27, , 1F
In this case your domain can be any connected
09/30 11:27, 1F
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09/30 11:28, , 2F
topological space
09/30 11:28, 2F
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09/30 20:39, , 3F
謝謝您!!
09/30 20:39, 3F
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