Preservation and reflection of properties acc and hacc

Maddalena Bonanzinga

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 147-153
  • ISSN: 0010-2628

Abstract

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The aim of the paper is to study the preservation and the reflection of acc and hacc spaces under various kinds of mappings. In particular, we show that acc and hacc are not preserved by perfect mappings and that acc is not reflected by closed (nor perfect) mappings while hacc is reflected by perfect mappings.

How to cite

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Bonanzinga, Maddalena. "Preservation and reflection of properties acc and hacc." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 147-153. <http://eudml.org/doc/247918>.

@article{Bonanzinga1996,
abstract = {The aim of the paper is to study the preservation and the reflection of acc and hacc spaces under various kinds of mappings. In particular, we show that acc and hacc are not preserved by perfect mappings and that acc is not reflected by closed (nor perfect) mappings while hacc is reflected by perfect mappings.},
author = {Bonanzinga, Maddalena},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {acc space; hacc space; countably compact space; ordinal space; cofinality; acc space; hacc space; countably compact space; ordinal space; cofinality},
language = {eng},
number = {1},
pages = {147-153},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Preservation and reflection of properties acc and hacc},
url = {http://eudml.org/doc/247918},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Bonanzinga, Maddalena
TI - Preservation and reflection of properties acc and hacc
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 147
EP - 153
AB - The aim of the paper is to study the preservation and the reflection of acc and hacc spaces under various kinds of mappings. In particular, we show that acc and hacc are not preserved by perfect mappings and that acc is not reflected by closed (nor perfect) mappings while hacc is reflected by perfect mappings.
LA - eng
KW - acc space; hacc space; countably compact space; ordinal space; cofinality; acc space; hacc space; countably compact space; ordinal space; cofinality
UR - http://eudml.org/doc/247918
ER -

References

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  2. Arhangel'skii A.V., Ponomarev V.I., Foundations of General Topology in Problems and Exercises (in Russian), Nauka, Moscow, 1974. MR0239550
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  6. Matveev M.V., A countably compact topological group which is not absolutely countably compact, Question and Answers 11 (1993), 173-176. (1993) Zbl0808.54025MR1234212
  7. Scott B.M., Towards a product theory for orthocompactness, Studies in Topology, eds. M. Stravrakas and K.R.Allen, Academic Press, Inc., New York, 1975, pp. 517-537. MR0372820
  8. van Douwen E.K., Reed G.M., Roscow A.W., Tree I.J., Star covering properties, Topology and Appl. 39 (1991), 71-103. (1991) MR1103993
  9. Vaughan J.E., Countably compact and sequentially compact spaces, in Handbook of Set-theoretic Topology, K.Kunen, J.E.Vaughan, eds., North-Holland, Amsterdam, 1984, pp. 569-602. Zbl0562.54031MR0776631
  10. Vaughan J.E., On the product of a compact space with an absolutely countably compact space, Commenationes Math. Univ. Carolinae, to appear. Zbl0917.54023MR1460834

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