Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min Li; Wang Guo-jun

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 4, page 801-814
  • ISSN: 0010-2628

Abstract

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In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

How to cite

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Li, Yong Min, and Guo-jun, Wang. "Localic Katětov-Tong insertion theorem and localic Tietze extension theorem." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 801-814. <http://eudml.org/doc/248051>.

@article{Li1997,
abstract = {In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.},
author = {Li, Yong Min, Guo-jun, Wang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {frame; locale; lower (upper) continuous chain; normal locale; frame; normal frame; real valued continuous function; locales; localic Urysohn lemma},
language = {eng},
number = {4},
pages = {801-814},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Localic Katětov-Tong insertion theorem and localic Tietze extension theorem},
url = {http://eudml.org/doc/248051},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Li, Yong Min
AU - Guo-jun, Wang
TI - Localic Katětov-Tong insertion theorem and localic Tietze extension theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 801
EP - 814
AB - In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.
LA - eng
KW - frame; locale; lower (upper) continuous chain; normal locale; frame; normal frame; real valued continuous function; locales; localic Urysohn lemma
UR - http://eudml.org/doc/248051
ER -

References

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  7. Li Yong-ming, Weak locale quotient morphisms and locally connected frames, J. Pure Appl. Alg. 110 (1996), 101-107. (1996) MR1390674
  8. Liu Yingming, Luo Maokang, Lattice-valued Hahn-Dieudonné-Tong insertion theorem and stratification structure, Top. Appl. 45 (1992), 173-178. (1992) Zbl0767.54016MR1180808
  9. Madden J.J., Frames associated with an abelian l -group, Trans. Amer. Math. Soc. 331 (1992), 265-279. (1992) Zbl0765.54029MR1042288
  10. Pultr A., Tozzi A., Equationally closed subframes and representation of quotient spaces, Cahiers Top. Geom. Diff. Cat. 33 (1993), 167-183. (1993) Zbl0789.54008MR1239466
  11. Tong H., Some characterization of normal and perfectly normal spaces, Bull. Amer. Math. Soc. 54 (1948), 65; see also Duke Math. Soc. 19 (1952), 248-292. (1948) MR0050265
  12. Vickers S., Topology Via Logic, Cambridge Press, Cambridge, 1989. Zbl0922.54002MR1002193

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