All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 324

Showing per page

Compositions of simple maps

Jerzy Krzempek (1999)

Fundamenta Mathematicae

A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple.  Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true...

Conditions which ensure that a simple map does not raise dimension

W. Dębski, J. Mioduszewski (1992)

Colloquium Mathematicae

The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...

Continuous selections, G δ -subsets of Banach spaces and usco mappings

Valentin G. Gutev (1994)

Commentationes Mathematicae Universitatis Carolinae

Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) G δ -subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.

Currently displaying 61 – 80 of 324