Geodesic
Shape dimension of maps
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 3-11.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{BASM_2018_1_a0,
     author = {P. S. Gevorgyan and I. Pop},
     title = {Shape dimension of maps},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--11},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2018_1_a0/}
}
TY  - JOUR
AU  - P. S. Gevorgyan
AU  - I. Pop
TI  - Shape dimension of maps
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2018
SP  - 3
EP  - 11
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2018_1_a0/
LA  - en
ID  - BASM_2018_1_a0
ER  - 
%0 Journal Article
%A P. S. Gevorgyan
%A I. Pop
%T Shape dimension of maps
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2018
%P 3-11
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2018_1_a0/
%G en
%F BASM_2018_1_a0
P. S. Gevorgyan; I. Pop. Shape dimension of maps. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 3-11. https://geodesic-test.mathdoc.fr/item/BASM_2018_1_a0/

[1] Borsuk K., “Concerning the notion of the shape of compact”, Proc. Intern. Symp. on Top. and its Appl. (Herceg-Novi, 1968), Savez Društava Mat., Fiz. i Astronom., Beograd, 1969, 98–104 | MR

[2] Borsuk K., Theory of shape, Lecture Notes Series, 28, Matematisk Ins. Aarhus Univ., 1971 | MR | Zbl

[3] Dydak J., “Some remarks concerning the Whithead theorem in shape theory”, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 23 (1975), 437–445 | MR | Zbl

[4] Gevorgyan P. S., Pop I., “Movability and Uniform Movability of Shape Morphisms”, Bulletin of the Polish Academy of Sciences. Mathematics, 64 (2016), 69–83 | MR | Zbl

[5] Gevorgyan P. S., Pop I., “On the $n$-movability of maps”, Topology and its Applications, 221 (2017), 309–325 | DOI | MR | Zbl

[6] Mardešić S., Segal J., Shape Theory. The Inverse System Approach, North-Holand, 1982 | MR | Zbl

[7] Nowak S., “Some properties of fundamental dimension”, Fund. Math., 85 (1974), 211–227 | DOI | MR | Zbl