CONTENTS Introduction................................................................. 5I. HOMOLOGY 1. Preliminaries............................................................. 7 2. Maps in spaces of finite type............................................. 9 3. The Čech homology functor with compact carriers........................... 11 4. Vietoris maps............................................................. 13 5. Homology of open subsets of Euclidean spaces.............................. 14II. THE LEFSCHETZ NUMBER 1. The (ordinary) Lefschetz number........................................... 18 2. The generalized Lefschetz number.......................................... 20III. MULTI-VALUED MAPS 1. Upper semi-continuous and compact multi-valued mapB....................... 24 2. Admissible maps........................................................... 26 3. Homotopy and selectors.................................................... 9 4. Lefschetz maps............................................................ 30IV. ANB-s, AANR-B and w-AANB-s 1. ANR-s..................................................................... 32 2. Approximation Theorem..................................................... 33 3. AANR-B.................................................................... 34 4. w-AANR-s.................................................................. 36V. THE LEFSCHETZ FIXED-POINT THEOREM 1. The index of coincidence.................................................. 37 2. The Lefschetz Fixed-Point Theorem for open subsets in ............... 40 3. The Lefschetz Fixed-Point Theorem for AANR-s.............................. 41 4. Neighbourhood fixed-point property........................................ 45 5. The Lefschetz Fixed-Point Theorem for w-AANR-s............................ 46 6. Two consequences of the Lefschetz Fixed-Point Theorem..................... 47VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE 1. Almost fixed points....................................................... 51 2. Fixed-point property for infinite products................................ 51
@book{bwmeta1.element.zamlynska-a7876602-92ed-4af8-a848-74505a8155d6,
author = {Lech G\'orniewicz},
title = {Homological methods in fixed-point theory of multi-valued maps},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1976},
zbl = {0324.55002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-a7876602-92ed-4af8-a848-74505a8155d6}
}
Lech Górniewicz. Homological methods in fixed-point theory of multi-valued maps. GDML_Books (1976), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-a7876602-92ed-4af8-a848-74505a8155d6/