When does the Katětov order imply that one ideal extends the other?
Paweł Barbarski; Rafał Filipów; Nikodem Mrożek; Piotr Szuca
Colloquium Mathematicae (2013)
- Volume: 130, Issue: 1, page 91-102
- ISSN: 0010-1354
Access Full Article
top
Abstract
topHow to cite
topPaweł Barbarski, et al. "When does the Katětov order imply that one ideal extends the other?." Colloquium Mathematicae 130.1 (2013): 91-102. <http://eudml.org/doc/283541>.
@article{PawełBarbarski2013,
abstract = {We consider the Katětov order between ideals of subsets of natural numbers ("$≤_\{K\}$") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which
$ ≤_\{K\} ⇒ ⊑ $
for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).},
author = {Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca},
journal = {Colloquium Mathematicae},
keywords = {Katětov order; rank of ideals; rank of filters; extending ideals; ideal convergence; Bolzano-Weierstrass property; BW property},
language = {eng},
number = {1},
pages = {91-102},
title = {When does the Katětov order imply that one ideal extends the other?},
url = {http://eudml.org/doc/283541},
volume = {130},
year = {2013},
}
TY - JOUR
AU - Paweł Barbarski
AU - Rafał Filipów
AU - Nikodem Mrożek
AU - Piotr Szuca
TI - When does the Katětov order imply that one ideal extends the other?
JO - Colloquium Mathematicae
PY - 2013
VL - 130
IS - 1
SP - 91
EP - 102
AB - We consider the Katětov order between ideals of subsets of natural numbers ("$≤_{K}$") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which
$ ≤_{K} ⇒ ⊑ $
for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).
LA - eng
KW - Katětov order; rank of ideals; rank of filters; extending ideals; ideal convergence; Bolzano-Weierstrass property; BW property
UR - http://eudml.org/doc/283541
ER -
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.