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<identifier>oai:HAL:hal-00699222v1</identifier>
<datestamp>2017-12-21</datestamp>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Approximation and fixed points for compositions of Rδ-maps</title>
<creator>Górniewicz, Lech</creator>
<creator>Lassonde, Marc</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 0166-8641</source>
<source>Topology and its Applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-00699222</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00699222</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00699222</source>
<source>Topology and its Applications, Elsevier, 1994, 55 (3), pp.239-250</source>
<language>en</language>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<subject>[MATH.MATH-GN] Mathematics [math]/General Topology [math.GN]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>A set-valued upper semi-continuous map is called an Rδ -map if each of its values is an Rδ -set (we recall that an Rδ -set is a space that can be represented as the intersection of a decreasing sequence of compact AR-spaces). We prove that a compact set-valued map of an AR-space into itself has a fixed point provided it can be factorized by an arbitrary finite number of Rδ -maps through ANR-spaces. This fact is a consequence of a more general result which is the main goal of this note. The proof relies on a refinement of the approximation technique and does not make use of homological tools.</description>
<date>1994</date>
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