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Low-dimensional topology usually deals with objects that are two-, three-, or four-dimensional in nature. Properly speaking, low-dimensional topology should be part of ...

The low-level language of topology, which is not really considered a separate "branch" of topology. Point-set topology, also called set-theoretic topology or general ...

The compact-open topology is a common topology used on function spaces. Suppose X and Y are topological spaces and C(X,Y) is the set of continuous maps from f:X->Y. The ...

A topological space is second countable if it has a countable topological basis.

Given a Hilbert space H, the sigma-strong operator topology is the topology on the algebra L(H) of bounded operators from H to itself defined as follows: A sequence S_i of ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...