New proofs of classical insertion theorems

Chris Good; Ian Stares

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 139-142
  • ISSN: 0010-2628

Abstract

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We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Katětov-Tong insertion theorem and we also discuss a proof of this.

How to cite

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Good, Chris, and Stares, Ian. "New proofs of classical insertion theorems." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 139-142. <http://eudml.org/doc/248608>.

@article{Good2000,
abstract = {We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Katětov-Tong insertion theorem and we also discuss a proof of this.},
author = {Good, Chris, Stares, Ian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {insertion of continuous functions; normality; countable paracompactness; perfect; insertion of continuous functions; normality; countable paracompactness; perfect normality},
language = {eng},
number = {1},
pages = {139-142},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {New proofs of classical insertion theorems},
url = {http://eudml.org/doc/248608},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Good, Chris
AU - Stares, Ian
TI - New proofs of classical insertion theorems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 139
EP - 142
AB - We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Katětov-Tong insertion theorem and we also discuss a proof of this.
LA - eng
KW - insertion of continuous functions; normality; countable paracompactness; perfect; insertion of continuous functions; normality; countable paracompactness; perfect normality
UR - http://eudml.org/doc/248608
ER -

References

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  11. Mandelkern M., A short proof of the Tietze-Urysohn extension theorem, Arch. Math. (Basel) 60 (1993), 364-366. (1993) Zbl0778.54005MR1206320
  12. Michael E., A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), 831-838. (1953) Zbl0052.18701MR0056905
  13. Michael E., Continuous selections I, Annals of Math. 63 (1956), 361-382. (1956) Zbl0071.15902MR0077107
  14. Rudin M.E., Dowker spaces, in: Handbook of Set-Theoretic Topology, North Holland, Amsterdam, 1984, pp.761-780. Zbl0566.54009MR0776636
  15. Scott B.M., A ``more topological'' proof of the Tietze-Urysohn theorem, Amer. Math. Monthly 85 (1988), 117-123. (1988) MR0474185
  16. Tong H., Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. (1952) Zbl0046.16203MR0050265

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