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In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape".
A 2009 study in developmental psychology examined non-cognitive traits including blood parameters and birth weight as well as certain cognitive traits, and concluded that "greater intrasex phenotype variability in males than in females is a fundamental aspect of the gender differences in humans".
In graph theory, two graphs and ′ are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of ′.If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the ...
A morphism of schemes is a universal homeomorphism if and only if it is integral, radicial and surjective. [1] In particular, a morphism of locally of finite type is a universal homeomorphism if and only if it is finite, radicial and surjective. For example, an absolute Frobenius morphism is a universal homeomorphism.
For example, if X is a topological space, then group elements are assumed to act as homeomorphisms on X. The structure of a G-space is a group homomorphism ρ : G → Homeo(X) into the homeomorphism group of X. Similarly, if X is a differentiable manifold, then the group elements are diffeomorphisms.
In psychology, personality type refers to the psychological classification of individuals. In contrast to personality traits , the existence of personality types remains extremely controversial. [ 1 ] [ 2 ] Types are sometimes said to involve qualitative differences between people, whereas traits might be construed as quantitative differences ...
The kernel and image of a homomorphism can be interpreted as measuring how close it is to being an isomorphism. The first isomorphism theorem states that the image of a group homomorphism, h(G) is isomorphic to the quotient group G/ker h. The kernel of h is a normal subgroup of G.