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happysauce
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Homework Statement
Let τ be a topology consisting of ∅, [itex]\Re[/itex][itex]^{2}[/itex] and complements of finite unions of points and lines. Is this a hausdorrf space?
Homework Equations
Just definition of Hausdorrf space
given a topological space X, the diagonal X[itex]\times[/itex]X is closed iff X is hausdorrf.
The Attempt at a Solution
My first thoughts were that every set in the space is an open set in the topology. Therefore, take the diagonal {(x,x) | x[itex]\in[/itex]X} and the complement of that. That will be open. therefore [itex]\Re[/itex] is hausdorrf in the space. And the product of hausdorrf space is hausdorrf so the topology is hausdorrf?