Geodesic
Cofinal completeness of the Hausdorff metric topology
Gerald Beer 1   ; Giuseppe Di Maio 2
1 Department of Mathematics California State University Los Angeles 5151 State University Drive Los Angeles, CA 90032, U.S.A.
2 Dipartimento di Matematica Facoltà di Scienze Seconda Università degli Studi di Napoli via Vivaldi 43 81100 Caserta, Italy
Fundamenta Mathematicae, Tome 208 (2010) no. 1, pp. 75-85 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/fm208-1-5
Keywords: net hausdorff uniform space called cofinally cauchy each entourage there exists cofinal rather residual set indices whose corresponding terms pairwise within entourage metric space equipped associated metric uniformity each cofinally cauchy sequence has cluster point does each cofinally cauchy net space called cofinally complete here necessary sufficient conditions nonempty closed subsets metric space equipped hausdorff distance cofinally complete

Gerald Beer  1   ; Giuseppe Di Maio  2

1 Department of Mathematics California State University Los Angeles 5151 State University Drive Los Angeles, CA 90032, U.S.A.
2 Dipartimento di Matematica Facoltà di Scienze Seconda Università degli Studi di Napoli via Vivaldi 43 81100 Caserta, Italy 
@article{10_4064_fm208_1_5,
     author = {Gerald Beer and Giuseppe Di Maio},
     title = {Cofinal completeness of the {Hausdorff} metric topology},
     journal = {Fundamenta Mathematicae},
     pages = {75--85},
     year = {2010},
     volume = {208},
     number = {1},
     doi = {10.4064/fm208-1-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm208-1-5/}
}
TY  - JOUR
AU  - Gerald Beer
AU  - Giuseppe Di Maio
TI  - Cofinal completeness of the Hausdorff metric topology
JO  - Fundamenta Mathematicae
PY  - 2010
SP  - 75
EP  - 85
VL  - 208
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm208-1-5/
DO  - 10.4064/fm208-1-5
LA  - en
ID  - 10_4064_fm208_1_5
ER  - 
%0 Journal Article
%A Gerald Beer
%A Giuseppe Di Maio
%T Cofinal completeness of the Hausdorff metric topology
%J Fundamenta Mathematicae
%D 2010
%P 75-85
%V 208
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm208-1-5/
%R 10.4064/fm208-1-5
%G en
%F 10_4064_fm208_1_5
Gerald Beer; Giuseppe Di Maio. Cofinal completeness of the Hausdorff metric topology. Fundamenta Mathematicae, Tome 208 (2010) no. 1, pp. 75-85. doi: 10.4064/fm208-1-5

Cité par Sources :