The theory of compact vector fields and some of its applications to topology of functional spaces (I)
- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1962
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topA. Granas. The theory of compact vector fields and some of its applications to topology of functional spaces (I). Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1962. <http://eudml.org/doc/268396>.
@book{A1962,
abstract = {§1-3 Lusternik [1] and Schnirelman, Borsuk [3]; see also Tucker [1], Krasnoselskiï [3] and Krein, Fan Ky [1, 2], Lefshetz [1].TABLE OF CONTENTSINTRODUCTION................................................................................................................................................................................................... 3PRELIMINARIES1. Metric spaces.................................................................................................................................................................................................... 52. Normed and Banach spaces......................................................................................................................................................................... 12CHAPTER I. Extension problems1. Extension of mappings. Tietze’s Extension Theorem.............................................................................................................................. 172. Homotopy, retraction and fixed point property............................................................................................................................................. 193. Essential and inessential mappings. Borsuk’s Antipodensatz and Brouwer’s Fixed Point Theorem........................................... 20CHAPTER II. Compact and finite dimensional mappings1. Approximation Theorem.................................................................................................................................................................................. 232. Examples of compact mappings.................................................................................................................................................................. 263. Extension of compact mappings................................................................................................................................................................... 28CHAPTER III. Compact vector fields and Homotopy Extension Theorem1. The space $(\mathfrak \{C\}(Y^X)$. Singularity free compact fields........................................................................................................... 322. Homotopy of compact vector fields............................................................................................................................................................... 343. Extension of compact fields and the Homotopy Extension Theorem.................................................................................................... 37CHAPTER IV. Essential and inessential compact fields. Theorems on Antipodes1. Essential and inessential compact fields. Schauder Fixed Point Theorem......................................................................................... 392. The First Theorem on Antipodes in Banach spaces................................................................................................................................ 413. The Second Theorem on Antipodes............................................................................................................................................................. 434. Alternative of Fredholm.................................................................................................................................................................................... 46CHAPTER V. Continuous continuation method and fixed-point theorems1. Continuous continuation method.................................................................................................................................................................. 482. Theorems on fixed points............................................................................................................................................................................... 50CHAPTER VI. Compact deformations. Theorem on the Sweeping. Birkhoff-Kellogg Theorem1. Separation between two points. Theorems on compact deformations................................................................................................ 542. Birkhoff-Kellogg Theorem.............................................................................................................................................................................. 563. Invariant directions for positive operators.................................................................................................................................................... 58},
author = {A. Granas},
keywords = {functional analysis},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {The theory of compact vector fields and some of its applications to topology of functional spaces (I)},
url = {http://eudml.org/doc/268396},
year = {1962},
}
TY - BOOK
AU - A. Granas
TI - The theory of compact vector fields and some of its applications to topology of functional spaces (I)
PY - 1962
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - §1-3 Lusternik [1] and Schnirelman, Borsuk [3]; see also Tucker [1], Krasnoselskiï [3] and Krein, Fan Ky [1, 2], Lefshetz [1].TABLE OF CONTENTSINTRODUCTION................................................................................................................................................................................................... 3PRELIMINARIES1. Metric spaces.................................................................................................................................................................................................... 52. Normed and Banach spaces......................................................................................................................................................................... 12CHAPTER I. Extension problems1. Extension of mappings. Tietze’s Extension Theorem.............................................................................................................................. 172. Homotopy, retraction and fixed point property............................................................................................................................................. 193. Essential and inessential mappings. Borsuk’s Antipodensatz and Brouwer’s Fixed Point Theorem........................................... 20CHAPTER II. Compact and finite dimensional mappings1. Approximation Theorem.................................................................................................................................................................................. 232. Examples of compact mappings.................................................................................................................................................................. 263. Extension of compact mappings................................................................................................................................................................... 28CHAPTER III. Compact vector fields and Homotopy Extension Theorem1. The space $(\mathfrak {C}(Y^X)$. Singularity free compact fields........................................................................................................... 322. Homotopy of compact vector fields............................................................................................................................................................... 343. Extension of compact fields and the Homotopy Extension Theorem.................................................................................................... 37CHAPTER IV. Essential and inessential compact fields. Theorems on Antipodes1. Essential and inessential compact fields. Schauder Fixed Point Theorem......................................................................................... 392. The First Theorem on Antipodes in Banach spaces................................................................................................................................ 413. The Second Theorem on Antipodes............................................................................................................................................................. 434. Alternative of Fredholm.................................................................................................................................................................................... 46CHAPTER V. Continuous continuation method and fixed-point theorems1. Continuous continuation method.................................................................................................................................................................. 482. Theorems on fixed points............................................................................................................................................................................... 50CHAPTER VI. Compact deformations. Theorem on the Sweeping. Birkhoff-Kellogg Theorem1. Separation between two points. Theorems on compact deformations................................................................................................ 542. Birkhoff-Kellogg Theorem.............................................................................................................................................................................. 563. Invariant directions for positive operators.................................................................................................................................................... 58
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/268396
ER -
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