The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

Oleg Okunev

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1750-1754
  • ISSN: 2391-5455

Abstract

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We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.

How to cite

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Oleg Okunev. "The one-point Lindelöfication of an uncountable discrete space can be surlindelöf." Open Mathematics 11.10 (2013): 1750-1754. <http://eudml.org/doc/269487>.

@article{OlegOkunev2013,
abstract = {We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.},
author = {Oleg Okunev},
journal = {Open Mathematics},
keywords = {Topology of pointwise convergence; The axiom; Lindelöf spaces; topology of pointwise convergence; the axiom},
language = {eng},
number = {10},
pages = {1750-1754},
title = {The one-point Lindelöfication of an uncountable discrete space can be surlindelöf},
url = {http://eudml.org/doc/269487},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Oleg Okunev
TI - The one-point Lindelöfication of an uncountable discrete space can be surlindelöf
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1750
EP - 1754
AB - We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.
LA - eng
KW - Topology of pointwise convergence; The axiom; Lindelöf spaces; topology of pointwise convergence; the axiom
UR - http://eudml.org/doc/269487
ER -

References

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  1. [1] Arhangel’skii A.V., Some problems and lines of investigation in general topology, Comment. Math. Univ. Carolin., 1988, 29(4), 611–629 
  2. [2] Arhangel’skii A.V., Problems in C p-theory, In: Open Problems in Topology, North-Holland, Amsterdam-New York-Oxford-Tokyo, 1990, 601–616 
  3. [3] Arhangel’skii A.V., Topological Function Spaces, Math. Appl. (Soviet Ser.), 78, Kluwer, Dordrecht-Boston-London, 1992 http://dx.doi.org/10.1007/978-94-011-2598-7[Crossref] 
  4. [4] Arhangel’skii A.V., Uspenskii V.V., On the cardinality of Lindelöf subspaces of function spaces, Comment. Math. Univ. Carolin., 1986, 27(4), 673–676 
  5. [5] Engelking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989 
  6. [6] Fremlin D.H., Consequences of Martin’s Axiom, Cambridge Tracts in Math., 84, Cambridge University Press, Cambridge, 1984 http://dx.doi.org/10.1017/CBO9780511896972[Crossref] Zbl0551.03033
  7. [7] Fuchino S., Shelah S., Soukup L., Sticks and clubs, Ann. Pure Appl. Logic, 1997, 90(1–3), 57–77 http://dx.doi.org/10.1016/S0168-0072(97)00030-4[Crossref] Zbl0890.03023

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