Shape dimension of maps
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GEVORGYAN, P., POP, I. Shape dimension of maps. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, vol. 86, nr. 1(86), pp. 3-11. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Volumul 86, Numărul 1(86) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322

Shape dimension of maps

CZU: 511.5+515.122
MSC 2010: 55P55, 54C56.

Pag. 3-11

Gevorgyan P.1, Pop I2
 
1 Moscow State Pedagogical University,
2 Alexandru Ioan Cuza University of Iaşi
 
Disponibil în IBN: 26 iulie 2018


Rezumat

In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The question of raising the shape dimension by shape finite-dimensional maps is solved. An example of a shape finite-dimensional surjective map between shape infinite-dimensional spaces is given.

Cuvinte-cheie
Dimension of a morphism of inverse systems, of a promorphism, shape dimension of a shape morphism, of a map.