[分析] 一題拓樸!

[comfiture (永和好地方)]

 A is open subset of R^n ，then 下列敘述：

 A∩cl(B) 包含於  cl(A∩B)  對所有B

 是否正確？



我反例找了蠻久找不到，

命題似乎是對的...

請拓樸高手幫個忙XD

感謝～

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.114.123.117
→ dogy007     :if x not in cl(A∩B), exist neighborhood V of x,
→ dogy007     :算了, 這樣似乎不好做
→ dogy007     :if x in A∩cl(B), x in A,exist neighborhood V ofx
→ dogy007     :V 包含於 A, since x in cl(B), exist x_n in B
→ dogy007     :lim x_n = x,for n large, x_n in A∩B
→ dogy007     :thus x in in cl(A∩B)
→ comfiture   :感謝D大的幫助~