## Viewing Algebraic Topology topics

The following topics are immediate sub-topics of Algebraic Topology.

• #### Term: Antipode

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• Definition: If x is a point of S^n (the unit n-sphere), then its antipode is the point -x.
• #### Term: Antipode Preserving

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• Definition: A map h: S^n -> S^m is said to be antipode-preserving if h(-x) = -h(x) for all x in S^n.
• #### Term: Arc

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• Definition: An arc A is a space homeomorphic to the unit interval [0, 1]. The end points of A are the two points and q of A such that A-p and A-q are connected; the other points of A are called interior poin...
• #### Term: Base Point

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• Definition: In a loop, the initial point of the path is the same as the end point of the path; it is called the base point.
• #### Term: Betti Number

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• Definition: If G is abelian and finitely generated, then there is a fundamental theorem to the effect that G is the direct sum of two subgroups, H and T. H is a free abelian of finite rank, and T is a subgroup...
• #### Term: Borsuk Lemma

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• Definition: Let a and b be points of S^2. Let A be a compact space, and let f: A -> S^2 -{a, b} be a continuous map. If f is nulhomotopic, then a and b lie in the same component of S^2 - f(A).
• #### Term: Borsuk Ulam Theorem

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• Definition: Given a continuous map f: S^(n+1) -> R^(n+1), there is a point x of S^(n+1) such that f(x) = f(-x).
• #### Term: Brouwer Fixed Point Theorem

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• Definition: Any continuous function g: B^n -> B^n has a fixed point, where B^n is the unit n-ball.
• #### Term: Coherent

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