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[] Separable Metric Space X: X is separable if YX such that

ClX(Y)=X

and Y is countable.

[] Cover of SX: A collection O of subsets of X is a cover of S in X if SO.

[] Open cover of SX: A collection O of subsets of X is an open cover of S in X if SO

and each member of O

is open in X.

[] Compact subset of X: A subset S is compact in X if every finite and infinite open cover of S in X

has a finite subset

that also covers S.

[] Totally bounded subset of X: A subset S is totally bounded in X if for any ε>0

a finite subset T of S such that

S{Nε,X(x):xT}.

[] Cauchy sequence in X: A sequence {xm}x is said to be cauchy if for each ε>0

a real number M(ε) such that

d(xk,xl)<ε

k, lM(ε) .

[] Complete Metric Space X: A metric space is complete if every cauchy sequence in X converges to a point in X.

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