Question

For the following set X and collection T of open subsets decide if the pair X,...

For the following set X and collection T of open subsets decide if the pair X, T satisfies the axioms of a topological space. If it does, determine whether X is connected. If it is not a topological space then explain which axioms fail.

X = Z and a subset U ⊂ Z is open if and only if its complement Z \ U is finite or U = ∅.

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O x- is connedles intopolos open set U,V orna u Sinte x-V, V X-U are afinite Setc, ant Then u- his inplies thol x is inite huhich ic oa -dion avid hence -thore does not exist an Paradion ox in topolo

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