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**Diamondlance** I'm looking at Munkres' Topology (2nd edition), trying to refresh myself on some of the basics. I'm having an issue with an early Lemma of his (Lemma 13.1), which states: Let X be a set, and let B be a basis for a topology T on X. Then T equals the collection of all unions of elements of B.

My issue with this is that any topology contains the empty set, but nothing about the definition* of a basis for a topology requires the empty set to be in B. Indeed, Munkres' proof of this Lemma ignores the empty set in T altogether. For this being such a well reputed book, I'm wondering if I'm missing something. Any thoughts?