Monotone normality and extension of functions

Ian Stares

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 563-578
  • ISSN: 0010-2628

Abstract

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We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of K 0 -spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.

How to cite

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Stares, Ian. "Monotone normality and extension of functions." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 563-578. <http://eudml.org/doc/247761>.

@article{Stares1995,
abstract = {We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of $K_0$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.},
author = {Stares, Ian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$; monotone normality; Tietze-Urysohn theorem; monotonically normal spaces},
language = {eng},
number = {3},
pages = {563-578},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Monotone normality and extension of functions},
url = {http://eudml.org/doc/247761},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Stares, Ian
TI - Monotone normality and extension of functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 563
EP - 578
AB - We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of $K_0$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.
LA - eng
KW - monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$; monotone normality; Tietze-Urysohn theorem; monotonically normal spaces
UR - http://eudml.org/doc/247761
ER -

References

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  1. Borges C.J.R., A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211-214. (1973) Zbl0257.54018MR0324644
  2. van Douwen E.K., Simultaneous extension of continuous functions, in Eric K. van Douwen, Collected Papers, Volume 1, J. van Mill, ed., North-Holland, Amsterdam, 1994. 
  3. Engelking R., General Topology, Sigma Series in Pure Mathematics, Vol. 6, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  4. Gartside P.M., Monotonicity in analytic topology, D. Phil. Thesis, Oxford University, 1993. 
  5. Gillman L., Jerison M., Rings of continuous functions, Van Nostrand, Princeton, N.J., 1960. Zbl0327.46040MR0116199
  6. Heath R.W., Lutzer D.J., Zenor P.L., Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. (1973) Zbl0269.54009MR0372826
  7. Mandelkern M., A short proof of the Tietze-Urysohn extension theorem, Arch. Math. (Basel) 60 (1993), 364-366. (1993) Zbl0778.54005MR1206320
  8. Moody P.J., Roscoe A.W., Acyclic monotone normality, Topology Appl. 47 (1992), 53-67. (1992) Zbl0801.54018MR1189992
  9. San-ou S., Characterizations of monotonically normal spaces, Questions and Answers in Gen. Top. 6 (1988), 117-123. (1988) Zbl0672.54017MR1045604
  10. Scott B.M., A ``more topological'' proof of the Tietze-Urysohn theorem, Amer. Math. Monthly 85 (1978), 192-193. (1978) Zbl0376.54006MR0474185
  11. Stares I.S., Extension of functions and generalised metric spaces, D. Phil. Thesis, Oxford University, June 1994. 

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