Science Quiz / Definitions in Analysis

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Can you name the object in Analysis from there definitions?

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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.
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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