Definition  Object 
Let E be a subset of X, then c in X is a ______ of E if, for all t>0 there exists an x in E such that t>d(x,c)  
Let (X,d), (Y,e) be metric spaces. Then f:X>Y is ______ at x0 if; for all t>0 there exist s>0 such that for all x in X, s>d(x,x0) implies t>e(f(x),f(x0))  
A sequence (x(n))in a metric space is a _____ if, for all t>0 there exists N, a natural number, such that (n,m >N) implies d(x(n),x(m))  
A subset E of X is ______ if, for all Cauchy sequences (x(n)) in E there exists an x in E such that x(n) > x as n > inf.  
A set E in X is said to be ____ in X if the closure of E is equal to X  
A metric space (X,d) is said to be _______ is it countains a countable dense subset.  
A point x in X is a _______ of a mapping T:X>X if T(x) = x.  
 Definition  Object 
A mapping T:X>X is a __________ if, there exists 0  
Let (X,d) be a metric space. A set E in X is ______ if every sequence in E has a subsequence that converges to a point in E.  
A set E in X is ______ if there do not exist set G1 and G2 such that, G1 intersect E and G2 intersect E do not equal the empty set, G1 and G2 cover E and G1 and G2 do not intersect  
A subset E in X is ___ if for any x and y in E there exists a continuous path from x to y in E.  
Fn:X>Y ______ if there exists F:X>Y such that for all t>0 the exist N such that n>N implies sup(d(Fn(x),F(x)),x)  
Let Fn:X>Y, then Fn ______ if there exist F:X>Y such that the d(Fn(x),F(x))>0 as n>Inf for all x in X  

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