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Let X={a,b,c,d}, A={ } be a subset of X, T={ ϕ,{a},{a,b},{a,b},X} be a topology on X. Find limit points

Let X={a,b,c,d} with the topology T={ ϕ,{a},{a,b},{a,b,c,d}}.Find close set.

Let X={a,b,c,d} with the topology T={ ϕ,{a},{a,b},{a,b,c,d}}.Find closure.

Q. Write and solve an example of closure of a set.

Let X={a,b,c,d} with the topology T={ ϕ,{a},{a,b},{a,b,c,d}}.Find closed set, subspace and closure.

true/false? prove.

1/2 is a limit of the interval ]− 2.5,1.5[

1/2 is a limit of the interval ]− 2.5,1.5[

Let X be a metric space, let K be a closed subset of X, and let x be in X-K. Prove that there exist disjoint open sets U and V such that U contains x and V contains K.

I need to prove whether these two topological spaces are homeomorphic: RP^2 and S^2\{∞}.

A space

d(X,T)

is called a discrete topological space if every subset of X is _________

d(X,T)

is called a discrete topological space if every subset of X is _________

Find a Peano Curve which fills out the unit square in E^2