Rodríguez Sanjurjo, José Manuel
(1986)
*On limits of shape maps.*
Topology and its Applications, 23
(2).
pp. 173-181.
ISSN 0166-8641

PDF
Restricted to Repository staff only until 31 December 2020. 618kB |

Official URL: http://www.sciencedirect.com/science/article/pii/0166864186900398

## Abstract

The notions of accessible and strongly accessible approximative maps are defined and studied. Approximative maps obtained as limits of sequences of shape equivalences are strongly accessible. It is proved that strongly accessible approximative maps induce pseudo-isomorphisms in the sense of H. Kato. It is also seen that, under the assumption of calmness, shape morphisms induced by accessible approximative maps are left invertible. As an application some results of L. Boxer concerning approximately invertible maps are generalized.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Hyperspaces; Special maps on topological spaces (open, closed, perfect, etc.); Compact (locally compact) absolute neighborhood retracts; Shape theory |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 17175 |

References: | B.J. Ball, Shapes of saturated subsets of compacta, Colloq. Math. 29 (1974) 241-246. K. Borsuk, Theory of shape, Monografie Matematyczne 59, Warszawa, 1975. K. Borsuk, Some quantitative properties of shapes, Fund. Math. 93 (1976) 197-212. L. Boxer, AANR’s and AR1 maps, Top. Proc. 6 (1981), 219-226. L. Boxer, Remarks on quasi-domination, Bull. Acad. Polon. Sci. 30 (1982) 553-558. L. Boxer, Maps related to calmness, Topology Appl. 15 (1983) 11-17. Z. Cerin, Homotopy properties of locally compact spaces ad infinity-calmness and smoothness, Pacific J. Math. 79 (1978) 69-91. Z. Cerin and A.P. Sostak, Some remarks on Borsuk’s fundamental metric, in: A. Czaszar, ed., Proc. Colloq. Topology, Budapest, 1978 (North-Holland, Amsterdam, 1980) 233-252. Z. Cerin, C-E-movable and (C, D)-E-tame compacta, Houston J. Math. 9 (1983), 9-27. J. Ford and J.W. Rogers, Refinable maps, Colloq. Math. 39 (1978) 263-269. H. Kato, Refinable maps in the theory of shape, Fund. Math. 113 (1981) 119-129. H. Kato, A remark on refinable maps and calmness, Proc. Amer. Math. Sot. 90 (1984) 649-652. A. Koyama, Note on quasi-domination in the sense of K. Borsuk, Proc. Japan Acad. 54 (1978) 151-154. V.F. Laguna and J.M.R. Sanjurjo, Spaces of approximative maps, preprint. S. MardeSiC, On Borsuk’s shape theory for compact pairs, Bull. Acad. Polon. Sci. 21 (1973) 1131-1136. S. MardeSiC and J. Segal, Shape Theory (North-Holland, Amsterdam, 1982). J.M.R. Sanjurjo, Algunas propiedades de tipo homotopico de 10s espacios FANR, An. Inst. Mat. UNAM 20 (1980) 113-125. |

Deposited On: | 22 Nov 2012 12:06 |

Last Modified: | 07 Feb 2014 09:43 |

Repository Staff Only: item control page