A fixed point theorem in o-minimal structures

Mário J. Edmundo[1]

  • [1] Universidade de Lisboa CMAF Av. Prof. Gama Pinto 2 1649-003 Lisboa (Portugal)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 5, page 1441-1450
  • ISSN: 0373-0956

Abstract

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Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps.

How to cite

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Edmundo, Mário J.. "A fixed point theorem in o-minimal structures." Annales de l’institut Fourier 57.5 (2007): 1441-1450. <http://eudml.org/doc/10264>.

@article{Edmundo2007,
abstract = {Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps.},
affiliation = {Universidade de Lisboa CMAF Av. Prof. Gama Pinto 2 1649-003 Lisboa (Portugal)},
author = {Edmundo, Mário J.},
journal = {Annales de l’institut Fourier},
keywords = {O-minimal structures; fixed point theorems; o-minimal structures},
language = {eng},
number = {5},
pages = {1441-1450},
publisher = {Association des Annales de l’institut Fourier},
title = {A fixed point theorem in o-minimal structures},
url = {http://eudml.org/doc/10264},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Edmundo, Mário J.
TI - A fixed point theorem in o-minimal structures
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 5
SP - 1441
EP - 1450
AB - Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps.
LA - eng
KW - O-minimal structures; fixed point theorems; o-minimal structures
UR - http://eudml.org/doc/10264
ER -

References

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  1. A. Berarducci, M. Otero, Transfer methods for o-minimal topology, J. Symbolic Logic 68 (2003), 785-794 Zbl1060.03059MR2000077
  2. J. Bochnak, M. Coste, M-F. Roy, Real algebraic geometry, (1998), Springer-Verlag Zbl0912.14023MR1659509
  3. G. W. Brumfiel, A Hopf fixed point theorem for semi-algebraic maps, (1992), Springer Verlag, Berlin Zbl0791.55003MR1226249
  4. M. Coste, An introduction to o-minimal geometry 
  5. H. Delfs, M. Knebusch, On the homology of algebraic varieties over real closed fields, J. reine u.angew. Math. 335 (1982), 122-163 Zbl0484.14006MR667464
  6. A. Dold, Lectures on algebraic topology, (1995), Springer Verlag Zbl0872.55001MR1335915
  7. L. van den Dries, Tame topology and o-minimal structures, (1998), Cambridge University Press Zbl0953.03045MR1633348
  8. M. Edmundo, M. Otero, Definably compact abelian groups, J. Math. Logic 4 (2004), 163-180 Zbl1070.03025MR2114966
  9. Y. Peterzil, C. Steinhorn, Definable compacteness and definable subgroups of o-minimal groups, J. London Math. Soc. 59 (1999), 769-786 Zbl0935.03047MR1709079
  10. J. Rotman, An introduction to algebraic topology, (1988), Springer Verlag Zbl0661.55001MR957919
  11. A. Woerheide, O-minimal homology, (1996) 

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