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[] Interior of a subset of X: Given any SX, the interior of S in X is

the largest open set InX(S) such that

InX(S)S.

[] Boundary of a subset of X: Given any SX, the boundary of S in X is

ClX(S)-InX(S) .

[] Convergent sequence in X: A sequence {xm}X converges to x*X if

for each ε>0

a real number M(ε) such that

d(xm,x*)<ε

mM(ε) .

[] Closed subset of X: A subset S is closed in X if, and only if,

any sequence all of whose terms are in S

converges to a point in S, if it converges at all.

[] Bounded subset of X: A subset S is bounded in X if

ε>0 such that

SNε,X(x)

for some xS.

[] Connected subset of X: A subset S is connected in X iff

S can not be written as SS1S2

where S1S2=

and S1, S2 are open in S.

[] Connected Metric Space X: X is connected iff the only clopen subsets of X are X and .

[] Dense subset of X: A subset Y is said to be dense in X if

ClX(Y)=X.

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