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The type of homology which results when the spaces being studied are restricted to simplicial complexes and subcomplexes.

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...

The continuous image of a Polish space, also called an analytic set.

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

An Abelian variety which is canonically attached to an algebraic variety which is the solution to a certain universal problem. The Albanese variety is dual to the Picard ...

A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...

The quartic with implicit equation x^4=x^2y-y^3. (1) The bow has vertical tangents at (+/-2/9sqrt(3),2/9) and horizontal tangents at (+/-1/4sqrt(2),1/4). Its curvature is ...

A clear-cut way of describing every object in a class in a one-to-one manner.

Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is ...