Topological calculus for separating points from closed sets by maps

Javier Gutiérrez García; Tomasz Kubiak

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 1, page 257-264
  • ISSN: 0011-4642

Abstract

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Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.

How to cite

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Gutiérrez García, Javier, and Kubiak, Tomasz. "Topological calculus for separating points from closed sets by maps." Czechoslovak Mathematical Journal 62.1 (2012): 257-264. <http://eudml.org/doc/246362>.

@article{GutiérrezGarcía2012,
abstract = {Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.},
author = {Gutiérrez García, Javier, Kubiak, Tomasz},
journal = {Czechoslovak Mathematical Journal},
keywords = {embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight; embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight},
language = {eng},
number = {1},
pages = {257-264},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Topological calculus for separating points from closed sets by maps},
url = {http://eudml.org/doc/246362},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Gutiérrez García, Javier
AU - Kubiak, Tomasz
TI - Topological calculus for separating points from closed sets by maps
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 257
EP - 264
AB - Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.
LA - eng
KW - embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight; embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight
UR - http://eudml.org/doc/246362
ER -

References

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  6. Kubiak, T., On L -Tychonoff spaces II, Fuzzy Sets Syst. 182 (2011), 21-36. (2011) MR2825771
  7. Kuratowski, K., Topology, Vol. I, New York-London: Academic Press; Warszawa: PWN---Polish Scientific Publishers. XX 560 (1966). (1966) Zbl0158.40901MR0217751
  8. Lane, S. Mac, Moerdijk, I., Sheaves in Geometry and Logic: A First Introduction to Topos Theory, New York etc.: Springer-Verlag 627 (1992). (1992) MR1300636
  9. Mrówka, S., 10.1007/BF02394609, Acta Math. 120 (1968), 161-185. (1968) Zbl0179.51202MR0226576DOI10.1007/BF02394609
  10. Sherman, D., 10.4169/000298910X476031, Am. Math. Mon. 117 (2010), 113-123. (2010) Zbl1210.54004MR2590191DOI10.4169/000298910X476031
  11. Sikorski, R., 10.4064/fm-36-1-165-206, Fundam. Math. 36 (1949), 165-206. (1949) Zbl0040.25204MR0036286DOI10.4064/fm-36-1-165-206
  12. Tychonoff, A., 10.1007/BF01782364, Math. Ann. 102 (1929), 544-561. (1929) MR1512595DOI10.1007/BF01782364

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