On minimal Hausdorff and minimal Urysohn functions

Filippo Cammaroto; Andrei Catalioto; Jack Porter

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1242-1251
  • ISSN: 2391-5455

Abstract

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In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.

How to cite

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Filippo Cammaroto, Andrei Catalioto, and Jack Porter. "On minimal Hausdorff and minimal Urysohn functions." Open Mathematics 9.6 (2011): 1242-1251. <http://eudml.org/doc/269017>.

@article{FilippoCammaroto2011,
abstract = {In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.},
author = {Filippo Cammaroto, Andrei Catalioto, Jack Porter},
journal = {Open Mathematics},
keywords = {P-function; Product function; H-closed function; U-closed function; Minimal Hausdorff function; Minimal Urysohn function; Hereditary and productive properties; -function; product function; -closed function; -closed function; minimal Hausdorff function; minimal Urysohn function; hereditary and productive properties},
language = {eng},
number = {6},
pages = {1242-1251},
title = {On minimal Hausdorff and minimal Urysohn functions},
url = {http://eudml.org/doc/269017},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Filippo Cammaroto
AU - Andrei Catalioto
AU - Jack Porter
TI - On minimal Hausdorff and minimal Urysohn functions
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1242
EP - 1251
AB - In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
LA - eng
KW - P-function; Product function; H-closed function; U-closed function; Minimal Hausdorff function; Minimal Urysohn function; Hereditary and productive properties; -function; product function; -closed function; -closed function; minimal Hausdorff function; minimal Urysohn function; hereditary and productive properties
UR - http://eudml.org/doc/269017
ER -

References

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  1. [1] Cammaroto F., On P-functions, In: Meeting Top. Spaces Theory Appl., Yatsushiro, 1999, 1–10 
  2. [2] Cammaroto F., Catalioto A., Porter J.R., On H-closed and U-closed functions (submitted) Zbl1274.54042
  3. [3] Cammaroto F., Fedorcuk V.V., Porter J.R., H-closed functions, Comment. Math. Univ. Carolin., 1998, 39(3), 563–572 Zbl0962.54011
  4. [4] Cammaroto F., Nordo G., On Urysohn, almost regular and semiregular functions, Filomat, 1994, 8, 71–80 Zbl0822.54007
  5. [5] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989 
  6. [6] Herrlich H., T v-Abgeschlossenheit und T v-Minimalität, Math. Z., 1965, 88(3), 285–294 http://dx.doi.org/10.1007/BF01111687 
  7. [7] Katětov M., Über H-abgeschlossene und bikompakte Räume, Časopis Pěst. Mat. Fys., 1940, 69, 36–49 
  8. [8] Nordo G., On product of P-functions, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur., 1994, 72, 465–478 
  9. [9] Pasynkov B.A., Extension to mappings of certain notions and assertions concerning spaces, In: Mappings and Functors, Moscow State University, Moscow, 1984, 72–102 (in Russian) 
  10. [10] Porter J.R., Woods R.G., Extensions and Absolutes of Hausdorff Spaces, Springer, New York, 1988 http://dx.doi.org/10.1007/978-1-4612-3712-9 
  11. [11] Stephenson R.M. Jr., Product of minimal Urysohn spaces, Duke Math. J., 1971, 38(4), 703–707 http://dx.doi.org/10.1215/S0012-7094-71-03885-3 Zbl0213.49401

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