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cianfa72

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- How to show that a "cross" in the plane is not a topological manifold for any n.

Hi, I've a doubt about the following example in "Introduction to Manifold" by L. Tu.

My understanding is that

However how can one show that there is not any other topology on the "cross" such that its intersection point ##p## is homeomorphic to some ##\mathbb R^n, n \geq 1## ?

Thank you.

My understanding is that

*if*one assumes the subspace topology from ##\mathbb R^2## for the "cross", then one can show that the topological space one gets is Hausdorff, second countable but non locally homeomorphic to any ##\mathbb R^n##.However how can one show that there is not any other topology on the "cross" such that its intersection point ##p## is homeomorphic to some ##\mathbb R^n, n \geq 1## ?

Thank you.