A . v b 26. 27. J. 31. 32. . A space is said to be second countable if and only if a. it has countable elements b. it has countable sub base , either (a) or (b) The diagonal A = {x x r: r X} is closed in X x X if and only if a. X is a Ty space b. X is a compact space c. X is a Hausdorff space In the cofinite topology on R. to what point or points does the sequence r,, = 1 converge? a. 0 b. 1 c. almost every point in R Let X and Y be topological spaces. Under which condition a function f: X =Y is said to be continuous a. If and only if preimages of open sets are open b. If open sets in X are mapped to open sets in Y e If closed sets in X are mapped to closed sets in Y . Let Y be a subset of X and I be a topology on X. Then the subspace topology U on Y induced by [ is defined as a U=(VeY:Vel) b.u={VeY:thereexists U Ist V=0UNY} . none of the above . In a topological space, a set is closed if and only if it is not open. a. True b, False The closure of a subset Y of a topological space is defined as the a. union of all the closed set containing the subset Y b. maximal closed set containing the subset Y . intersection of all the closed set containing the subset Y let be a topological space (X, ) .Then the closure of is a. X b. not defined C. r'.' let A and B be subsets of a topological space (X, I'). Then the closure of AUB s s AUB b. AUB c. AuB