Another approach to dimension of maps

• Autorzy: Krzempek, J.
• Języki publikacji: EN

Abstrakty

EN

Two equivalent definitions of the Cech-Lebesgue dimension are extended to closed (continuous) maps. This leads to two different dimension-like functions: the covering dimension and partition dimension of maps. A few characterizations of at most n-dimensional maps (for both dimensions) are proved as well as countable and locally finite sum theorems.

Słowa kluczowe

PL

odwzorowanie domknięte; podział; pokrycie; wymiar

EN

at most k-to-one map (=map of order is less than or equal k); closed map; cover; dimension; partition

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 2
• Strony: 141-154
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Krzempek, J.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] S. A. Bogatyĭ, M. Madirimov, On the dimension theory of metrizable spaces with periodic homeomorphisms (in Russian), Mat. Sb., 98 (1975) 72-83, 158.
• [2] D. Buhagiar, Fiberwise generał topology: a brief outlook, Topology Atlas Invited Contributions 5 (2000), URL http:\\at.yorku.ca\t\a\i\c\34.htm.
• [3] R. Engelking, General topology, PWN, Warszawa 1977.
• [4] R. Engelking, Theory of dimensions, finite and infinite, Heldermann, Lemgo 1995.
• [5] J. Krzempek, Compositions of simple maps, Fund. Math., 162 (1999) 149-162.
• [6] B. A. Pasynkov, On the dimension and geometry of mappings (in Russian), Dokl. Akad. Nauk SSSR, 221 (1975) 543-546.
• [7] B. A. Pasynkov, Extension to mappings of certain notions and assertions concerning spaces (in Russian), in: Mappings and functors, Moscow State Univ., Moscow (1984) 72-102.
• [8] B. A. Pasynkov, On the geometry of continuous mappings of finite-dimensional metrizable compacta (in Russian), Tr. Mat. Inst. Steklova, 212 (1996) 147-172.
• [9] J. Suzuki, Note on a theorem for dimension, Proc. Japan Acad., 35 (1959) 201-202.
• [10] I. A. Vaĭnšteĭn, On closed mappings (in Russian), Moskov. Gos. Univ. Učenye Zapiski Matematika, 155 (1952) 3-53.