Homological methods in fixed-point theory of multi-valued maps

Górniewicz, Lech

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Homological methods in fixed-point theory of multi-valued maps

Autorzy

Lech Górniewicz

Seria

Rozprawy Matematyczne tom/nr w serii: 129 wydano: 1976

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Abstrakty

CONTENTS
  Introduction................................................................. 5
I. 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.............................. 14
II. THE LEFSCHETZ NUMBER
  1. The (ordinary) Lefschetz number........................................... 18
  2. The generalized Lefschetz number.......................................... 20
III. 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............................................................ 30
IV. ANB-s, AANR-B and w-AANB-s
  1. ANR-s..................................................................... 32
  2. Approximation Theorem..................................................... 33
  3. AANR-B.................................................................... 34
  4. w-AANR-s.................................................................. 36
V. THE LEFSCHETZ FIXED-POINT THEOREM
  1. The index of coincidence.................................................. 37
  2. The Lefschetz Fixed-Point Theorem for open subsets in $R^n$............... 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..................... 47
VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE
  1. Almost fixed points....................................................... 51
  2. Fixed-point property for infinite products................................ 51

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 129

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CXXIX

Daty

wydano

1976

Twórcy

autor

Lech Górniewicz

Bibliografia

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