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A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any ...

The Heine-Borel theorem states that a subspace of R^n (with the usual topology) is compact iff it is closed and bounded. The Heine-Borel theorem can be proved using the ...

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats ...

A weakened version of pointwise convergence hypothesis which states that, for X a measure space, f_n(x)->f(x) for all x in Y, where Y is a measurable subset of X such that ...

The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.

Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

An interval in which one endpoint is included but not the other. A half-closed interval is denoted [a,b) or (a,b] and is also called a half-open interval. The non-standard ...

Let M be a sigma-algebra M, and let lambda_1 and lambda_2 be measures on M. If there exists a pair of disjoint sets A and B such that lambda_1 is concentrated on A and ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

A function f defined on a subset S subset R^n is said to be pseudoconcave if -f is pseudoconvex.