On the preservation of separation axioms in products

Milan Z. Grulović; Miloš S. Kurilić

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 4, page 713-721
  • ISSN: 0010-2628

Abstract

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We give sufficient and necessary conditions to be fulfilled by a filter and an ideal in order that the -quotient space of the -ideal product space preserves -properties () (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.

How to cite

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Grulović, Milan Z., and Kurilić, Miloš S.. "On the preservation of separation axioms in products." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 713-721. <http://eudml.org/doc/247370>.

@article{Grulović1992,
abstract = {We give sufficient and necessary conditions to be fulfilled by a filter $\Psi $ and an ideal $\Lambda $ in order that the $\Psi $-quotient space of the $\Lambda $-ideal product space preserves $T_k$-properties ($k=0,1,2,3,3\frac\{1\}\{2\}$) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.},
author = {Grulović, Milan Z., Kurilić, Miloš S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {separation axioms; box product; ultraproduct; ideal product topology; separation axiom; box product; ultraproduct; Tikhonov product},
language = {eng},
number = {4},
pages = {713-721},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the preservation of separation axioms in products},
url = {http://eudml.org/doc/247370},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Grulović, Milan Z.
AU - Kurilić, Miloš S.
TI - On the preservation of separation axioms in products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 713
EP - 721
AB - We give sufficient and necessary conditions to be fulfilled by a filter $\Psi $ and an ideal $\Lambda $ in order that the $\Psi $-quotient space of the $\Lambda $-ideal product space preserves $T_k$-properties ($k=0,1,2,3,3\frac{1}{2}$) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.
LA - eng
KW - separation axioms; box product; ultraproduct; ideal product topology; separation axiom; box product; ultraproduct; Tikhonov product
UR - http://eudml.org/doc/247370
ER -

References

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  1. Bankston P., Ultraproducts in topology, Gen. Topology Appl. 7 (1977), 283-308. (1977) Zbl0364.54005MR0458351
  2. van Douwen E.K., The box product of countably many metrizable spaces need not be normal, Fundamenta Mathematicae LXXXVIII.2 (1975), 127-132. (1975) MR0385781
  3. Engelking R., General Topology, PWN - Polish Scientific Publishers, 1977. Zbl0684.54001MR0500780
  4. Kelly J.L., General Topology, Springer Verlag, Graduate Texts in Mathematics 27. 
  5. Knight C.J., Box topologies, Quart. J. Math. Oxford 15 (1964), 41-54. (1964) Zbl0122.17404MR0160184

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