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  1. M

    Metric spaces

    Here’s a problem I’ve been struggling with, for a while…. If (X,d) is a metric space and f:X-->X is a continuous function, then show that A={ x in X : f(x)=x} is a closed set. One possible way that I can think of is defining a new function g(x) = f(x)-x .Then A={x in X : g(x) =0}. Now {0} is...
  2. M

    Find the subgroup!

    well...thanks a lot, sir!! i figured it out...
  3. M

    Find the subgroup!

    thanks sir, but could you please elaborate further. i don't seem to get the idea...
  4. M

    Find the subgroup!

    let p and q be distinct primes. suppose that H is a proper subset of integers and H is a group under addition that contains exactly 3 elements of the set { p,p+q,pq, p^q , q^p}. Determine which of the foll are the 3 elements in H a. pq, p^q, q^p b. P+q, pq,p^q c. p, p+q, pq d. p...