迪倫X asked in 科學數學 · 1 decade ago

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

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  • 1 decade ago
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    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

    Source(s): me
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