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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) where x·y is vector multiplication which is assumed to be bilinear. Now define ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

The minimum excluded value. The mex of a set S of nonnegative integers is the least nonnegative integer not in the set.

A level set in three dimensions.

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...

A definition of a set by mentioning a defining property.

A set in a Polish space is a Borel set iff it is both analytic and coanalytic. For subsets of w, a set is delta_1^1 iff it is "hyperarithmetic."

A T_1-space is a topological space fulfilling the T1-separation axiom: For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y ...

The set theory symbol (aleph) for the cardinal number of a well-orderable infinite set.

A partially ordered set P is a circle order if it is isomorphic to a set of disks ordered by containment.