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Characteristic classes are cohomology classes in the base space of a vector bundle, defined through obstruction theory, which are (perhaps partial) obstructions to the ...

A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The ith Chern class is an obstruction to the ...

A topology is given by a collection of subsets of a topological space X. The smallest topology has two open sets, the empty set emptyset and X. The largest topology contains ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, then there exists a B_3 in S such ...

A topological space X has a one-point compactification if and only if it is locally compact. To see a part of this, assume Y is compact, y in Y, X=Y\{y} and x in X. Let C be ...

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x ...

An n-dimensional open disk of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Krantz (1999, p. 3) uses the symbol D(x,r) ...

Let A be a finite-dimensional power-associative algebra, then A is the vector space direct sum A=A_(11)+A_(10)+A_(01)+A_(00), where A_(ij), with i,j=0,1 is the subspace of A ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...