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One of the Eilenberg-Steenrod axioms. Let X be a single point space. H_n(X)=0 unless n=0, in which case H_0(X)=G where G are some groups. The H_0 are called the coefficients ...

A lattice which satisfies the identities (x ^ y) v (x ^ z)=x ^ (y v z) (x v y) ^ (x v z)=x v (y ^ z) is said to be distributive.

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

A partial order defined by (i-1, i), (i+1, i) for odd i.

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...

An interval in which one endpoint is included but not the other. A half-closed interval is denoted [a,b) or (a,b] and is also called a half-open interval. The non-standard ...

If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

An inaccessible cardinal is a cardinal number which cannot be expressed in terms of a smaller number of smaller cardinals.

A lattice which is built up of layers of n-dimensional lattices in (n+1)-dimensional space. The vectors specifying how layers are stacked are called glue vectors. The order ...

A lattice embedding is a one-to-one lattice homomorphism.