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# 高微證明題(關於多變數連續方程式)

let f:Rn->Rm If Bis a subset of Rm, we let f(-1)(B)={x屬於Rn:f(x)屬於B}

f(-1)(B)si called the preimage of B under f

please show that if f is continuous and FㄈRm is closed, then the

preimage f(-1)(F) is closed

拜託各位高手幫忙

### 1 Answer

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- Scharze spaceLv 71 decade agoFavorite Answer
http://tw.knowledge.yahoo.com/question/question?qi...

我之前寫的證明 參考看看吧

只要將過程中的開區間改成|| ||的符號即可

Closed的話

f is continuous and F is contained in R^m, then R^m\F is open

so f^(-1)(R^m\F)=R^n\f^(-1)(F) is open

That is , f^(-1)(F) is closed

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