Extension of multisequences and countably uniradial classes of topologies

Szymon Dolecki; Andrzej Starosolski; Stephen W. Watson

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 1, page 165-181
  • ISSN: 0010-2628

Abstract

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It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter ℋ on ω , the class of ℋ -radial topologies contains each sequential topology, then it includes the class of subsequential topologies.

How to cite

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Dolecki, Szymon, Starosolski, Andrzej, and Watson, Stephen W.. "Extension of multisequences and countably uniradial classes of topologies." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 165-181. <http://eudml.org/doc/249173>.

@article{Dolecki2003,
abstract = {It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter $\mathcal \{H\}$ on $\omega $, the class of $\mathcal \{H\}$-radial topologies contains each sequential topology, then it includes the class of subsequential topologies.},
author = {Dolecki, Szymon, Starosolski, Andrzej, Watson, Stephen W.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sequential cascade; multisequence; subsequential topology; countably uniradial; Arens topologies of higher order; sequential cascade; multisequence; subsequential topology; countably uniradial},
language = {eng},
number = {1},
pages = {165-181},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extension of multisequences and countably uniradial classes of topologies},
url = {http://eudml.org/doc/249173},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Dolecki, Szymon
AU - Starosolski, Andrzej
AU - Watson, Stephen W.
TI - Extension of multisequences and countably uniradial classes of topologies
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 165
EP - 181
AB - It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter $\mathcal {H}$ on $\omega $, the class of $\mathcal {H}$-radial topologies contains each sequential topology, then it includes the class of subsequential topologies.
LA - eng
KW - sequential cascade; multisequence; subsequential topology; countably uniradial; Arens topologies of higher order; sequential cascade; multisequence; subsequential topology; countably uniradial
UR - http://eudml.org/doc/249173
ER -

References

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