continuous homomorphism

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• Homomorphism — In abstract algebra, a homomorphism is a structure preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the Greek language: ὁμός (homos) meaning same and μορφή (morphe)… …   Wikipedia

• Continuous functions on a compact Hausdorff space — In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), is a vector… …   Wikipedia

• Induced homomorphism — In mathematics, an induced homomorphism is a structure preserving map between a pair of objects that is derived in a canonical way from another map between another pair of objects. A particularly important case arises in algebraic topology, where …   Wikipedia

• Induced homomorphism (fundamental group) — In mathematics, especially in the area of topology known as algebraic topology, the induced homomorphism is a group homomorphism related to the study of the fundamental group.DefinitionLet X and Y be topological spaces; let x 0 be a point of X… …   Wikipedia

• Group homomorphism — In mathematics, given two groups ( G , *) and ( H , ·), a group homomorphism from ( G , *) to ( H , ·) is a function h : G → H such that for all u and v in G it holds that: h(u*v) = h(u) h(v) where the group operation on the left hand side of the …   Wikipedia

• Induced homomorphism (algebraic topology) — In mathematics, especially in the area of topology known as algebraic topology, an induced homomorphism is a way of relating the algebraic invariants of topological spaces which are already related by a continuous function. Such homomorphism… …   Wikipedia

• Degree of a continuous mapping — This article is about the term degree as used in algebraic topology. For other uses, see degree (mathematics). A degree two map of a sphere onto itself. In topology, the degree is a numerical invariant that describes a continuous mapping between… …   Wikipedia

• Chern–Weil homomorphism — In mathematics, the Chern–Weil homomorphism is a basic construction in the Chern–Weil theory, relating for a smooth manifold M the curvature of M to the de Rham cohomology groups of M, i.e., geometry to topology. This theory of Shiing Shen Chern… …   Wikipedia

• Covering group — This article is about topological covering group. For algebraic covering group, see universal perfect central extension. In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and… …   Wikipedia

• Zonal spherical function — In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K invariant vector in an… …   Wikipedia

• Bohr compactification — In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G . Its importance lies in the reduction of the theory of uniformly almost periodic functions on G …   Wikipedia