Uniformly movable categories and uniform movability of topological spaces

• Autorzy: Gevorgyan P. S. , Pop I.
• Języki publikacji: EN

Abstrakty

EN

A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the horaotopy category HTop over the subcategory HPol of polyhedra is uniformly movable. This is a weakened version of the categorical notion of uniform movability introduced by the second author.

Słowa kluczowe

EN

shape theory; uniformly movable inverse system (space); uniformly movable category

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 3
• Strony: 229--242
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Gevorgyan P. S.

autor

Pop I.

• Department of Higher Mathematics, Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya, 14 111250 Moscow, Russia,

Bibliografia

• [1] K. Borsuk, On movable compacta, Fund. Math. 66 (1969/70), 137-146.
• [2] P. S. Gevorgyan, Movable categories, Glasnik Mat. Ser. Ill 38 (58) (2003), 177-183.
• [3] —, Movable categories and movability of topological spaces, to appear.
• [4] S. Mardešić and J. Segal, Movable compacta and ANR-systems, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 18 (1970), 649-654.
• [5] —, —, Shape Theory. The Inverse System Approach, North-Holland, 1982.
• [6] M. Moszyńska, Uniformly movable compact spaces and their algebraic properties Fund. Math. 77 (1972), 125-144.
• [7] I. Pop, A categorical notion of movability, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Ser. Noua Mat. 49 (2003), 327-341.