Cofinal completeness of the Hausdorff metric topology

Gerald Beer, and Giuseppe Di Maio. "Cofinal completeness of the Hausdorff metric topology." Fundamenta Mathematicae 208.1 (2010): 75-85. <http://eudml.org/doc/282903>.

@article{GeraldBeer2010,
abstract = {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.},
author = {Gerald Beer, Giuseppe Di Maio},
journal = {Fundamenta Mathematicae},
keywords = {Hausdorff distance; cofinal completeness; uniform paracompactness; local compactness; measure of local compactness.},
language = {eng},
number = {1},
pages = {75-85},
title = {Cofinal completeness of the Hausdorff metric topology},
url = {http://eudml.org/doc/282903},
volume = {208},
year = {2010},
}

TY - JOUR
AU - Gerald Beer
AU - Giuseppe Di Maio
TI - Cofinal completeness of the Hausdorff metric topology
JO - Fundamenta Mathematicae
PY - 2010
VL - 208
IS - 1
SP - 75
EP - 85
AB - 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.
LA - eng
KW - Hausdorff distance; cofinal completeness; uniform paracompactness; local compactness; measure of local compactness.
UR - http://eudml.org/doc/282903
ER -