# Spaces of approximative maps. II

### Impacto

Laguna, V. F. and Rodríguez Sanjurjo, José Manuel (1986) Spaces of approximative maps. II. Publicacions Matemàtiques, 30 (2-3). pp. 115-126. ISSN 0214-1493

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http://www.uab.cat/matematiques/Organisation

## Abstract

The authors study the space $A\sp*(X,Y)$ of all approximative maps f$=\{f\sb k: X\to Y\}$ between compact subsets X, Y of the Hilbert cube. The topology of this space is given by the pseudometric $d\sp*(\underline f,\underline g)=\inf \{\sup \{dist(f\sb k,g\sb k)\vert$ $k\ge k'\}\vert$ $k'=1,2,...\}$. They show that approximative maps from the same path component of $A\sp*(X,Y)$ induce the same shape morphism, but the converse implication does not hold. They also consider several classes of approximative maps which form closed subsets of $A\sp*(X,Y)$.

Item Type: Article space of approximative maps between compact subsets of the Hilbert cube; shape morphism Sciences > Mathematics > Topology 21955 19 Jun 2013 16:16 12 Dec 2018 15:14