Short proofs of two theorems in topology

Mohammad Ismail; Andrzej Szymański

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 539-541
  • ISSN: 0010-2628

Abstract

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We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A T 1 weakly δ θ -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.

How to cite

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Ismail, Mohammad, and Szymański, Andrzej. "Short proofs of two theorems in topology." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 539-541. <http://eudml.org/doc/247510>.

@article{Ismail1993,
abstract = {We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A $T_1$ weakly $\delta \theta $-refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.},
author = {Ismail, Mohammad, Szymański, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {countably compact; initially $\kappa $-compact; weakly $\delta \theta $-refinable; $\kappa $-refinable; sequential; weakly -refinable countably compact space},
language = {eng},
number = {3},
pages = {539-541},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Short proofs of two theorems in topology},
url = {http://eudml.org/doc/247510},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Ismail, Mohammad
AU - Szymański, Andrzej
TI - Short proofs of two theorems in topology
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 539
EP - 541
AB - We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A $T_1$ weakly $\delta \theta $-refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
LA - eng
KW - countably compact; initially $\kappa $-compact; weakly $\delta \theta $-refinable; $\kappa $-refinable; sequential; weakly -refinable countably compact space
UR - http://eudml.org/doc/247510
ER -

References

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  1. Arhangel'skiĭ A.V., The star method, new classes of spaces and countable compactness, Soviet Math. Dokl. 21 (1980), 550-554. (1980) MR0569369
  2. Burke D.K., Covering properties, Handbook of Set Theoretic Topology, North Holland, 1984, pp. 347-422. Zbl0569.54022MR0776628
  3. Ostaszewski A.J., Compact σ -metric Hausdorff spaces are sequential, Proc. Amer. Math. Soc. 68 (1978), 339-343. (1978) Zbl0392.54014MR0467677
  4. Stephenson R.M., Jr., Initially κ -compact and related spaces, Handbook of Set Theoretic Topology, North Holland (1984), pp. 603-632. Zbl0588.54025MR0776632
  5. Wicke H.H., Worrell J.M., Jr., Point countability and compactness, Proc. Amer. Math. Soc. 55 (1976), 427-431. (1976) Zbl0323.54013MR0400166

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