| Title:
|
On locally $r$-incomparable families of infinite-dimensional Cantor manifolds (English) |
| Author:
|
Chatyrko, Vitalij A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
165-173 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Cantor manifolds |
| Keyword:
|
countable-dimensional |
| Keyword:
|
weakly infinite-dimensional |
| Keyword:
|
\newline strongly infinite-dimensional |
| MSC:
|
54F45 |
| MSC:
|
57N99 |
| idZBL:
|
Zbl 1060.54510 |
| idMR:
|
MR1715209 |
| . |
| Date available:
|
2009-01-08T18:50:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119070 |
| . |
| Reference:
|
[A-P] Aleksandrov P.S., Pasynkov B.A.: Introduction to Dimension Theory (in Russian).Moscow, 1973. |
| Reference:
|
[KB] Borsuk K.: Theory of Retracts.PWN, Warszawa, 1969. Zbl 0153.52905 |
| Reference:
|
[PB] Borst P.: Classification of weakly infinite-dimensional spaces, Part I: A transfinite extension of the covering dimension.Fund.Math. 130 (1988), 1-25. MR 0964160 |
| Reference:
|
[Ch1] Chatyrko V.A.: Analogues of Cantor manifolds for transfinite dimensions (in Russian).Mat. Zametki 42 (1987), 115-119. MR 0910034 |
| Reference:
|
[Ch2] Chatyrko V.A.: On hereditarily indecomposable non-metrizable continua (in Russian).Mat. Zametki 46 (1989), 122-125. MR 1032919 |
| Reference:
|
[E] Engelking R.: Theory of Dimensions Finite and Infinite.Sigma Series in Pure Math. vol.10, Heldermann Verlag, 1995. Zbl 0872.54002, MR 1363947 |
| Reference:
|
[F1] Fedorchuk V.V.: Bicompacta with non-coinciding dimensionalities (in Russian).DAN SSSR 182 (1968), 275-277. MR 0234432 |
| Reference:
|
[F2] Fedorchuk V.V.: Mappings that do not reduce dimension (in Russian).DAN SSSR 185 (1969), 54-57. |
| Reference:
|
[H1] Henderson D.W.: An infinite-dimensional compactum with no positive-dimensional compact subsets - a simpler construction.Amer. J. Math. 89 ((1967), 105-123. MR 0210072 |
| Reference:
|
[H2] Henderson D.W.: A lower bound for transfinite dimension.Fund. Math. 64 (1968), 167-173. Zbl 0167.51301, MR 0243496 |
| Reference:
|
[O] Olszewski W.: Cantor manifolds in the theory of transfinite dimension.Fund. Math. 145 (1994), 39-64. Zbl 0813.54025, MR 1295159 |
| Reference:
|
[EP] Pol E.: On infinite-dimensional Cantor manifolds.Topology Appl. 71 (1996), 265-276. Zbl 0864.54029, MR 1397945 |
| Reference:
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[RP1] Pol R.: Questions in Dimension Theory, Open Problems in Topology.North-Holland, 1990. MR 1078654 |
| Reference:
|
[RP2] Pol R.: A weakly infinite-dimensional compactum which is not countable-dimensional.Proc. Amer. Math. Soc. 82 (1981), 634-636. Zbl 0469.54014, MR 0614892 |
| Reference:
|
[R-S-W] 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. MR 0519716 |
| Reference:
|
[T] Tumarkin L.A.: On Cantorian manifolds of an infinite number of dimensions (in Russian).DAN SSSR 115 (1957), 244-246. MR 0091454 |
| Reference:
|
[T-H] Tsuda K., Hata M.: Fractional dimension function.Topology Proc. 18 (1993), 323-328. MR 1305140 |
| . |
