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A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

The American Mathematical Society awards two prizes named in honor of Prof. Frank Nelson Cole, a senior member of the AMS who made a bequest to the society in 1928 upon his ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

Five or six Wolf prizes are awarded yearly to outstanding living scientists and artists for achievements in the interest of mankind and friendly relations among peoples. In ...

Given a subspace A of a space X and a map from A to a space Y, is it possible to extend that map to a map from X to Y?

A fiber space, depending on context, means either a fiber bundle or a fibration.

The canonical generator of the nonvanishing homology group on a topological manifold.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.