# Monotone normality and extension of functions

Commentationes Mathematicae Universitatis Carolinae (1995)

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

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topStares, 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

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

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