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algebraic topology

terms from algebraic topology

TermDefinition
topological space (X) contains empty set, X; closed under intersection, closed under union
homeomorphism (f: X -> Y) continuous bijection (continuous, 1-1, onto, continuous inverse)
homeomorphic (X, Y) X, Y are equivalent in the topological sense
path connected (x, y \in X) for all x, y in X, there is a continuous function f: [0, 1] -> X such that f(0) = x and f(1) = y
Hausdorff for any x, y \in X, exist disjoint open sets U, V containing x, y respectively; think "housed off"
Created by: its.mahon
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