Please undelete the following question: https://math.stackexchange.com/questions/4141455/union-of-closed-convex-sets/4141589#4141589 The question and (my - to be fair) answer was highly upvoted. The question was closed/deleted for lack of context. I edited the question to include some context: The claim seems to be true in situations one can immediately think of. It is one example of a claim on convex sets that seems to be true, but isn't.