Sentence examples for has a countable base of from inspiring English sources

Our assumptions on Y imply that it has a countable base of connected open sets.

(This is stated as Corollary 2 in [30].) Let X be a topological space which has a countable base, let Γ be a family of nonempty closed subsets of X, and suppose every descending sequence in Γ is bounded below by a member of Γ.

Specifically, a space X is said to be first countable if each point has a countable neighborhood basis (local base).

This problem has a countable system of eigenvalues and as.

In the limit we obtain a model that is continuum-like in important respects, yet it has a countable set of agents with a finitely additive, 'uniform' distribution.

These systems do not extend the language with any probabilistic operators, but rather deal with a "classical" propositional language L, which has a countable set of atomic propositions, and the usual truth-functional (Boolean) connectives.

Recall that a topological space is first countable if each point has a countable (decreasing) local base.

Hence, if (3) has any model, it has a countable model, which is in fact a submodel of the original.

Nonetheless, a strong metatheorem asserts that any set of formulas that has a model, has a countable (finite or denumerable) model.

As for set theory, the failure of categoricity was already taken note of by Skolem in 1923, because it follows from the Löwenheim-Skolem Theorem (which Skolem arrived at that year; see Skolem 1923, based on Löwenheim 1915 and Skolem 1920): any first order theory in a countable language that has a model has a countable model.

We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum.