MATH PUZZLE DU JOUR A 1-manifold is a topological space in which every point has a neighborhood homeomorphic to the open real interval (0,1). This definition omits the “Hausdorff condition“ (any two points have disjoint neighborhoods). Why is that condition important here?
Because it’s redundant? If every point has such a neighborhood than the Haussdorf condition must be also met?
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No. If the condition is not there, you may be allowing some weird spaces which you don’t really want. How many 1-dimensional manifolds do you think there are?
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