Definitions for

**"homogeneous"**When items or entities in a group are similar. opposite of heterogeneous.

Of the same kind of nature; consisting of similar parts, or of elements of the like nature; -- opposed to heterogeneous; as, homogeneous particles, elements, or principles; homogeneous bodies.

Possessing the same number of factors of a given kind; as, a homogeneous polynomial.

A space ''X'' is homogeneous if, for every ''x'' and ''y'' in ''X'', there is a homeomorphism ''f'' : ''X'' â†’ ''X'' such that ''f''(''x'') = ''y''. Intuitively, the space looks the same at every point. Every topological group is homogeneous.

A space is homogeneous if for every and in there is a homeomorphism : - such that () = . Intuitively speaking, this means that the space looks the same at every point. All topological groups are homogeneous.

Genetic description of open pollinated varieties. When all (or most) genes are paired up with their identical genes, so that reproduction (seed set) results in offspring with very similar characteristics. Traditionally achieved through several generations of self-pollinating. In the laboratory homogeneity (homozygosity) can be created in one generation with doubled haploid technology See genotype See double haploid See homozygous

Composed of identical cell types.

The same in structure and quality; similar or identical.

A homogeneous system of linear equations is a system of linear equations without constant terms. A homogeneous matrix vector equation has form Ax=0. Note that a homogeneous linear system is always consistent, as it always has the solution x=0 (the trivial solution).

A term describing a mixture that is the same throughout, as for example when sugar is fully dissolved in water. A solution is a homogenous mixture.

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, Dn is the domain of f and for some element r of the range of f, every member of Sn is mapped to r. That is, f is constant on the n-tuples of elements of S.

Spatial data of one feature type such as points, lines, or regions.

(Spatial User's Guide and Reference; search in this book)

Having common demographics, attitudes, purchase patterns, and needs.

Similar throughout (referring to the snow pack).

the same at all locations. Homogenized milk is not separated into cream and milk.

Exhibiting a high degree of homogeneity.

Connected networks that use the bridging method.

containing a single phase.

A soil mass with the same properties in all directions.