A set is open if and only if every point in the set has an open neighbourhood contained within the set

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Flesh out and clean up, then demote to grade B
See page 25 in Lee's top manifolds, there's a bunch of equivalent conditions. However I do think there's a more general neighbourhood one, if I could just be bothered to prove, "a set is open if and only if it is neighbourhood to all of its points" or something


Let [ilmath](X,\mathcal{ J })[/ilmath] be a topological space, then[1]:


Grade: B
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  1. Introduction to Topological Manifolds - John M. Lee