Online Quiz on Compact Space

Every compact subspace of a Hausdorff space is . . . . . . . . . . . . .

(a)  

The product of finitely many compact space is . . . . . . . .

(a)  

Let f be bijective continuous from X to Y. If X is compact and Y is Hausdroff, then f is a . .. . . . . . . .

(a)  

Every closed interval in R is compact . . . . . . .

(a)  

Let (X, d) be a metric space and A be a nonempty subset of X. For each x in X, the distance from x to A is

(a)  

Let f be continuous map of the metric space X to the metric space Y. Then f is . . . . . . .

(a)  

A point x in a space X is said to be an isolated point of X if one point set {x} is . . . . . . . in X.

(a)  

If a nonempty compact Hausdorff space X has no isolated points, then X is . . . . . . . . .

(a)