On locally r -incomparable families of infinite-dimensional Cantor manifolds

Vitalij A. Chatyrko

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 165-173
  • ISSN: 0010-2628

Abstract

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The notion of locally r -incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally r -incomparable families of different types of finite-dimensional Cantor manifolds.

How to cite

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Chatyrko, Vitalij A.. "On locally $r$-incomparable families of infinite-dimensional Cantor manifolds." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 165-173. <http://eudml.org/doc/248377>.

@article{Chatyrko1999,
abstract = {The notion of locally $r$-incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally $r$-incomparable families of different types of finite-dimensional Cantor manifolds.},
author = {Chatyrko, Vitalij A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Cantor manifolds; countable-dimensional; weakly infinite-dimensional; strongly infinite-dimensional; Cantor manifold; countable-dimensional; weakly infinite-dimensional; strongly infinite-dimensional},
language = {eng},
number = {1},
pages = {165-173},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On locally $r$-incomparable families of infinite-dimensional Cantor manifolds},
url = {http://eudml.org/doc/248377},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Chatyrko, Vitalij A.
TI - On locally $r$-incomparable families of infinite-dimensional Cantor manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 165
EP - 173
AB - The notion of locally $r$-incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally $r$-incomparable families of different types of finite-dimensional Cantor manifolds.
LA - eng
KW - Cantor manifolds; countable-dimensional; weakly infinite-dimensional; strongly infinite-dimensional; Cantor manifold; countable-dimensional; weakly infinite-dimensional; strongly infinite-dimensional
UR - http://eudml.org/doc/248377
ER -

References

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  11. Olszewski W., Cantor manifolds in the theory of transfinite dimension, Fund. Math. 145 (1994), 39-64. (1994) Zbl0813.54025MR1295159
  12. Pol E., On infinite-dimensional Cantor manifolds, Topology Appl. 71 (1996), 265-276. (1996) Zbl0864.54029MR1397945
  13. Pol R., Questions in Dimension Theory, Open Problems in Topology, North-Holland, 1990. MR1078654
  14. Pol R., A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), 634-636. (1981) Zbl0469.54014MR0614892
  15. Rubin L.R., Schori R.M., Walsh J.J., New dimension-theory techniques for constructing infinite-dimensional examples Gen. Topology Appl., 10 (1979), 93-102. (1979) MR0519716
  16. Tumarkin L.A., On Cantorian manifolds of an infinite number of dimensions (in Russian), DAN SSSR 115 (1957), 244-246. (1957) MR0091454
  17. Tsuda K., Hata M., Fractional dimension function, Topology Proc. 18 (1993), 323-328. (1993) MR1305140

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