quantum123
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Is every subspace of a connected space connected?
mathwonk said:this is the most clueless question I've heard yet. reveals a complete lack of understanding of connectedness. presumably the questioner is learning by reading some worthless book with no examples or useful explanations at all.
(I waS IN exactly this boat when i was beginning topology, after hearing continuity defined as inverse image of opens are open. that is totally useless in understanding homeomorphisms. after that i still thought a sphere might be homeomorphic to a torus.)
Yes, the subset you mentioned is not connected with the usual or euclidean topology. But what about the induced or subspace topology where every open set is defined to be an intersection of that particular subset and a particular open set in the usual topology?StatusX said:For a counterexample, take the real line, and the subset of the real line formed by removing a point.
quantum123 said:Yes, the subset you mentioned is not connected with the usual or euclidean topology. But what about the induced or subspace topology where every open set is defined to be an intersection of that particular subset and a particular open set in the usual topology?
quantum123 said:We are talking about topology and mathematics here.
So is it better to stick to the topic and not talk about something else like for example, me?