homogeneous elements
1Homogeneous — Ho mo*ge ne*ous, a. [Gr. ?; ? the same + ? race, kind: cf. F. homog[ e]ne. See {Same}, and {Kin}.] 1. Of the same kind of nature; consisting of similar parts, or of elements of the like nature; opposed to heterogeneous; as, homogeneous particles …
2homogeneous — [hō΄mō jē′nē əs, hō΄məjē nē əs; häm΄ōjē′nē əs, häm΄əjē′nē əs] adj. [ML homogeneus < Gr homogenēs, of the same race or kind: see HOMO & GENUS] 1. the same in structure, quality, etc.; similar or identical 2. composed of similar or identical… …
3Homogeneous space — In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A… …
4Homogeneous polynomial — In mathematics, a homogeneous polynomial is a polynomial whose terms are monomials all having the same total degree; or are elements of the same dimension. For example, x^5 + 2 x^3 y^2 + 9 x^1 y^4 is a homogeneous polynomial of degree 5, in two… …
5Homogeneous coordinate ring — In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring R = K[X0, X1, X2, ..., XN]/I where I is the homogeneous ideal… …
6homogeneous — homogeneously, adv. /hoh meuh jee nee euhs, jeen yeuhs, hom euh /, adj. 1. composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population. 2. of the same kind or nature; essentially alike. 3. Math. a.… …
7homogeneous — ho•mo•ge•ne•ous [[t]ˌhoʊ məˈdʒi ni əs, ˈdʒin yəs, ˌhɒm ə [/t]] adj. 1) gen composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population[/ex] 2) of the same kind or nature; essentially alike 3) Math. a)… …
8Homogeneous (large cardinal property) — In the context of a large cardinal property, a subset, S , of D is homogeneous for a function f means that for some natural number n , D n is the domain of f and for some element r of the range of f , every member of S n is mapped to r . That is …
9homogeneous — I (Roget s IV) modif. Syn. uniform, unvaried, comparable, similar, analogous, of a piece, much of a muchness*; see also alike 2 , like . II (Roget s 3 Superthesaurus) (VOCABULARY WORD) a. [HO mo JEE nee us] made of like or similar elements. A… …
10homogeneous — Of uniform structure or composition throughout. [homo + G. genos, race] * * * ho·mo·ge·neous jē nē əs, nyəs adj of uniform structure or composition throughout ho·mo·ge·neous·ly adv ho·mo·ge·neous·ness n * * * ho·mo·ge·ne·ous (ho″mo je …
