Cofinal completeness of the Hausdorff metric topology

• Autorzy: Gerald Beer , Giuseppe Di Maio
• Języki publikacji: EN

Abstrakty

EN

A net in a Hausdorff uniform space is called cofinally Cauchy if for each entourage, there exists a cofinal (rather than residual) set of indices whose corresponding terms are pairwise within the entourage. In a metric space equipped with the associated metric uniformity, if each cofinally Cauchy sequence has a cluster point, then so does each cofinally Cauchy net, and the space is called cofinally complete. Here we give necessary and sufficient conditions for the nonempty closed subsets of the metric space equipped with Hausdorff distance to be cofinally complete.

Kategorie tematyczne

• 54E45: Compact (locally compact) metric spaces
• 54E35: Metric spaces, metrizability
• 54B20: Hyperspaces
• 54E50: Complete metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 208
• Numer: 1
• Strony: 75-85

Daty

wydano

2010

Twórcy

autor

Gerald Beer

• Department of Mathematics, California State University Los Angeles, 5151 State University Drive, Los Angeles, CA 90032, U.S.A.

autor

Giuseppe Di Maio

• Dipartimento di Matematica, Facoltà di Scienze, Seconda Università degli Studi di Napoli, via Vivaldi 43, 81100 Caserta, Italy

Identyfikatory

DOI

10.4064/fm208-1-5