On Cantor manifolds for the small transfinite dimension

• Autorzy: Reńska M.
• Języki publikacji: EN

Abstrakty

EN

We show that some of the spaces X_(L) constructed in [7] are Cantor manifolds for the small transfinite dimension trind, which is transfinite extension of the Menger-Urysohn dimension. That gives us the construction of such spaces that is simpler than constructions of metrizable Cantor manifolds for trind published hitherto. In addition, our examples are disjoint unions of Euclidean cubes and the irrationals.

Słowa kluczowe

EN

Cantor manifolds; small transfinite dimension

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 2
• Strony: 163--168
• Opis fizyczny: bibliogr. 9 poz.

Twórcy

autor

Reńska M.

• Institute of Mathematics, University of Warsaw Banacha 2, 02-097 Warsaw, Poland,

Bibliografia

• [1] V. A. Chatyrko, Counterparts of Cantor manifolds for transfinite dimensions, Mat. Zametki 42 (1987) 115-119 (in Russian).
• [2] R. Engelking, Theory of Dimensions Finite and Infinite, Heldermann Verlag, Lemgo 1995.
• [3] R. Engelking and K. Sieklucki, Topology. A Geometric Approach, Heldermann Verlag, Berlin 1992.
• [4] W. Olszewski, Universal spaces in the theory of transfinite dimension I, Fund. Math. 144 (1994), 243-258.
• [5] W. Olszewski, Cantor manifolds in the theory of transfinite dimension, Fund. Math. 145 (1994), 39-64.
• [6] E. Pol, On infinite-dimensional Cantor manifolds, Topology and Appl. 71 (1996), 265-276.
• [7] M. Re´nska On Cantor manifolds for the large transfinite dimension, Topology Appl. 112 (2001), 1-11.
• [8] J. M. Smirnov, On universal spaces for certain classes of infinite-dimensional spaces (in Russian), Izv. Akad. Nauk SSSR 23 (1959), 185-196; English translation: Amer. Math. Soc. Transl. 2(21) (1962), 35-50.
• [9] G. H. Toulmin, Shuffling ordinals and transfinite dimensions, Proc. London Math. Soc. 4 (1954), 177-195.