Main Article Content
On the Metrization Lemma for Uniform Spaces
Abstract
We show a numeric generalization of the well-known metrization
lemma for uniform spaces, thereby answering a question left open in [2] to
the affirmative. An application of the new lemma in the setting of approach
theory yields the conclusion that every approach uniformity has a basis of
pseudo-metrics.
Mathematics Subject Classification (1991): 54E15, 54E35
Keywords: metrization, uniform space, approach uniform space, metric
spaces, metrizability, uniform structures and generalizations, uniform spaces,
open
Quaestiones Mathematicae 24(1) 2001, 123–128
lemma for uniform spaces, thereby answering a question left open in [2] to
the affirmative. An application of the new lemma in the setting of approach
theory yields the conclusion that every approach uniformity has a basis of
pseudo-metrics.
Mathematics Subject Classification (1991): 54E15, 54E35
Keywords: metrization, uniform space, approach uniform space, metric
spaces, metrizability, uniform structures and generalizations, uniform spaces,
open
Quaestiones Mathematicae 24(1) 2001, 123–128
