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A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...

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

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

A Reeb component is a Reeb foliation (M,F) whose leaves are proper. A foliation which has no Reeb components is said to be Reebless.

A foliation which has no Reeb components is said to be Reebless.

A Reinhardt domain with center c is a domain D in C^n such that whenever D contains z_0, the domain D also contains the closed polydisk.

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 ...

In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

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