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A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

A complemented lattice is an algebraic structure (L, ^ , v ,0,1,^') such that (L, ^ , v ,0,1) is a bounded lattice and for each element x in L, the element x^' in L is a ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

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 ...

Consider a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then the Herbrand universe H of S is defined by the following rules. 1. All constants ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

An ordinal number alpha>0 is called a limit ordinal iff it has no immediate predecessor, i.e., if there is no ordinal number beta such that beta+1=alpha (Ciesielski 1997, p. ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...