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Discussion :: GATE Mathematics

  1. Consider the following statements: 
    P: The family of subsets {An = (-1/n, 1/n), n = 1, 2, ...} satisfies the finite intersection property. 
    Q: On an infinite set X , a metric d : X * X --> R is defined as d(x,y) = [0 , x = y and 1, x â‰  y] The metric space (X,d) is compact. 
    R: In a Frechet (T1) topological space, every finite set is closed. 
    S: If f : R --> X is continuous, where R is given the usual topology and (X, t) is a Hausdorff (T2) space, then f is a one-one function. 
    Which of the above statements are correct?
    2. A.
    P and R
    B.
    P and S
    C.
    R and S
    D.
    Q and S

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    Answer : Option A

    Explanation :

    -NA-

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