[微積] Continuous function

[hotcom (臣又又-Chanyoyo)]

Suppose f: R^n -> R is a continuous function . Show that the set

[x屬於R^n的元素│f(x)=0]  is a closed set.


求提點 @@

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◆ From: 1.169.128.156
→ THEJOY      :法一:證明{x|f(x)>0},{x|f(x)<0} are open
→ THEJOY      :法二：S is closed <=> S的closure = S來證
→ THEJOY      :主要用連續性的定義或性質就能簡單證明出來了
推 secjmy      :在你那個集合挑一個收斂點列收斂到x*，去證明f(x*)=0
→ yeh6        :連續函數把closed set拉回closed set
→ hotcom      :謝謝喔 會証了^_^