Let X = { a, b, c }, define a topology on X as open sets are {empty set, {b}, {a, b}, {b, c}, X}. Then I want to know the homotopy type of this space. Is it contractile?
2026-03-25 04:18:50.1774412330
Homotopy Type of some space
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That space is contractible, indeed.
I suggest you read J. Barmak's book on finite topological spaces to learn how to prove this easily.