Homotopies and the Universal Fixed Point Property
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Homotopies and the Universal Fixed Point Property. / Szymik, Markus.
I: Order: A Journal on the Theory of Ordered Sets and its Applications, Bind 32, Nr. 3, 2015, s. 301-311.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Homotopies and the Universal Fixed Point Property
AU - Szymik, Markus
PY - 2015
Y1 - 2015
N2 - A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points that is continuous whenever the self-map varies continuously. To even specify the problem, we introduce the universal fixed point property. Our results apply in particular to the analysis of convex subspaces of Banach spaces, to the topology of finite-dimensional manifolds and CW complexes, and to the combinatorics of Kolmogorov spaces associated with finite posets.
AB - A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points that is continuous whenever the self-map varies continuously. To even specify the problem, we introduce the universal fixed point property. Our results apply in particular to the analysis of convex subspaces of Banach spaces, to the topology of finite-dimensional manifolds and CW complexes, and to the combinatorics of Kolmogorov spaces associated with finite posets.
KW - Finite poset
KW - Fixed point property
KW - Homotopy
KW - Kolmogorov space
UR - http://www.scopus.com/inward/record.url?scp=84944351337&partnerID=8YFLogxK
U2 - 10.1007/s11083-014-9332-x
DO - 10.1007/s11083-014-9332-x
M3 - Journal article
AN - SCOPUS:84944351337
VL - 32
SP - 301
EP - 311
JO - Order
JF - Order
SN - 0167-8094
IS - 3
ER -
ID: 161394114