Rectangular covers of products missing diagonals

Yukinobu Yajima

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 147-153
  • ISSN: 0010-2628

Abstract

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We give a characterization of a paracompact Σ -space to have a G δ -diagonal in terms of three rectangular covers of X 2 ∖ Δ . Moreover, we show that a local property and a global property of a space X are given by the orthocompactness of ( X × β X ) ∖ Δ .

How to cite

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Yajima, Yukinobu. "Rectangular covers of products missing diagonals." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 147-153. <http://eudml.org/doc/247606>.

@article{Yajima1994,
abstract = {We give a characterization of a paracompact $\Sigma $-space to have a $G_\delta $-diagonal in terms of three rectangular covers of $X^2\setminus \Delta $. Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X\times \beta X)\setminus \Delta $.},
author = {Yajima, Yukinobu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\Sigma $-space; $G_\delta $-diagonal; $\sigma $-closure-preserving; $\sigma $-cushioned; rectangular cover; orthocompact; metacompact; Fréchet space; rectangular cover; paracompact -space; orthocompact space; metacompact space; Fréchet space; -diagonal; diagonal},
language = {eng},
number = {1},
pages = {147-153},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Rectangular covers of products missing diagonals},
url = {http://eudml.org/doc/247606},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Yajima, Yukinobu
TI - Rectangular covers of products missing diagonals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 147
EP - 153
AB - We give a characterization of a paracompact $\Sigma $-space to have a $G_\delta $-diagonal in terms of three rectangular covers of $X^2\setminus \Delta $. Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X\times \beta X)\setminus \Delta $.
LA - eng
KW - $\Sigma $-space; $G_\delta $-diagonal; $\sigma $-closure-preserving; $\sigma $-cushioned; rectangular cover; orthocompact; metacompact; Fréchet space; rectangular cover; paracompact -space; orthocompact space; metacompact space; Fréchet space; -diagonal; diagonal
UR - http://eudml.org/doc/247606
ER -

References

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  1. Arhangel'skiĭ A.V., Kombarov A.P., On ∇ -normal spaces, Topology and Appl. 35 (1990), 121-126. (1990) MR1058792
  2. Chaber J., Čoban M., Nagami N., On monotonic generalizations of Moore spaces, Čech-complete spaces, and p -spaces, Fund. Math. 83 (1974), 107-119. (1974) MR0343244
  3. Gruenhage G., Generalized metric spaces, Handbook of Set-theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 423-501. Zbl0794.54034MR0776629
  4. Gruenhage G., Pelant J., Analytic spaces and paracompactness of X 2 ∖ Δ , Topology and Appl. 28 (1988), 11-15. (1988) Zbl0636.54025MR0927277
  5. Junnila H.J.K., Metacompactness, paracompactness and interior-preserving open covers, Trans. Amer. Math. Soc. 249 (1979), 373-385. (1979) Zbl0404.54017MR0525679
  6. Junnila H.J.K., On submetacompactness, Topology Proc. 3 (1978), 375-405. (1978) MR0540503
  7. Kombarov A.P., On rectangular covers of X 2 ∖ Δ , Comment. Math. Univ. Carolinae 30 (1989), 81-83. (1989) MR0995704
  8. Nagami K., Σ -spaces, Fund. Math. 65 (1969), 169-192. (1969) Zbl0181.50701MR0257963
  9. Yajima Y., A characterization of submetacompactness in terms of products, Proc. Amer. Math. Soc. 112 (1991), 291-296. (1991) Zbl0722.54017MR1054165
  10. Yajima Y., Subspaces of squares; X 2 ∖ Δ and others, Abstracts of Short Conference of Uniform Mathematics and its Applications, Bern, 1991. 

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