Prove that t1 is strictly finer than t2

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Let X be an infinite set with the finite complement topology. Let T1 denote the product to topology on X*X and let T2 dent the finite complement topology on X*X. Prove that T1 is strictly finer than T2. Consider the subset of R2, X= ( {0} x [0,1] U [0,1] x {0} ). Show the dictionary order topology on X and the subspace topology on X are not comparable by finding a set that are in one but the other and vice versa.

Reference no: EM13868114

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