3 edition of **Homological methods in fixed-point theory of multi-valued maps** found in the catalog.

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

Lech GГіrniewicz

- 205 Want to read
- 31 Currently reading

Published
**1976**
by Państwowe Wydawn. Naukowe in Warszawa
.

Written in English

- Fixed point theory,
- Set-valued maps,
- Homology theory

**Edition Notes**

Statement | Lech Górniewicz. |

Series | Dissertationes mathematicae = Rozprawy matematyczne -- 129, Rozprawy matematyczne -- 129. |

The Physical Object | |
---|---|

Pagination | 71 p. : |

Number of Pages | 71 |

ID Numbers | |

Open Library | OL13627324M |

OCLC/WorldCa | 2678723 |

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. L. Górniewicz, Homological methods in fixed point theory of multi-valued maps, Dissertationes Math. Warsaw (), L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Acad. Publ., Dordrecht-Boston-London, Author: Nasreddine Mohamed Benkafadar, Boris Danielovich Gel'man.

GGRNIEWICZ L., Homological methods in fixed-point theory of multi-valued maps, Diasertationes Mathemot- i (). HOCKETT H. & HOLMES P., Josephson junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets, Ergod. Topological Fixed Point Theory of Multivalued Mappings - Ebook written by Lech Górniewicz. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Topological Fixed Point Theory of .

Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work. With an appendix, “Infinite-dimensional cohomology and bifurcation theory”, by Kazimierz Gęba. MR ; Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, MR ; Wojciech Kryszewski, Topological and approximation methods of degree theory of set-valued maps, Dissertationes Math.

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Homological methods were initiated in by S. Eilenberg and In this chapter we would like to present a systematic study of the fixed point theory for multivalued maps by using homological by: In the paper the integer-valued fixed-point index theory for compositions of set-valued maps having proximally -connected values satisfying all the axioms of a fixed point index is presented.

Thus in Chapter III the approximation (on the graph) method in fixed point theory of multi valued mappings is presented. Chapter IV is devoted to the homo logical methods and contains more general results, e. g., the Lefschetz Fixed Point Theorem, the fixed point index and the topological degree theory.

This book is an attempt to give a systematic presentation of results and meth ods which concern the fixed point theory of multivalued mappings and some of its applications.

In selecting the material Homological Methods in Fixed Point Theory of Multivalued Mappings. Lech Górniewicz. [32] L. Górniewicz, Fixed point theorems for multi-valued maps of special ANR-s, University of Gdańsk, 1 (), pp.

[33] L. Górniewicz, Asymptotic fixed point theorems for multi-valued maps, Symp. of Topology, Tbilisi Homological methods in the fixed-point theory of multi-valued maps. The infinite-dimensional case. § Partitions and the cohomology defined by them. § The topological characteristic of a multi-valued vector field in a Banach space.

§ The rotation of almost acyclic multi-valued vector fields. § Cited by: Guide to the literature in Chapter II Chapter III. Homological methods in the fixed-point theory of multi-valued maps.

The infinite-dimensional case § Partitions and the cohomology defined by them § The topological characteristic of a multi-valued vector field in a Banach space § The rotation of almost acyclic multi-valued vector fields § Computation of the topological characteristic and.

_____, On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts, J. Math. Anal. Appl. (), – MathSciNet CrossRef zbMATH Google ScholarCited by: 6.

This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework.

Additional Physical Format: Online version: Górniewicz, Lech. Homological methods in fixed-point theory of multi-valued maps. Warszawa: Państwowe Wydawn. Let be a subset of a topological vector space and let be a set-valued map from into such that for each finite subset of and for each is Homological methods in fixed-point theory of multi-valued maps, Dissertationes Math.

(Rozprawy Mat Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 47H On the other hand, it is well known that the topological degree theory (which is very close to the fixed-point index theory) for convex-valued mappings may be built by the use of a very simple method, namely, by an approximation of a given multi-valued mapping on the graph by a Cited by: mer School on Homological Methods in Commutative Algebra organised by the Tata Institute of Fundamental Research in The audience consisted of teachers and research students from Indian universities who desired to have a general introduction to the subject.

The lectures were given by an, Balwant Singh and ran. THAN. The algebraic map M is non-degenerate (or without boundary) if each of the involutions a, b, c act fixed point freely on B; otherwise the union of the fixed points of a, b and c is called the boundary of M.

The group G=〈a,b,c〉 is called the monodromy group of M, and M is said to be connected if Cited by: 5. Massimo Furi, Maria Patrizia Pera, Marco Spadini. Pages On the Existence of Equilibria and Fixed Points of Maps under Constraints. The purpose of this paper is to survey the fixed point theory of two very special classes of multivalued maps with weights which were found during the intense research activity of that time.

APPROXIMATIVE METHODS IN THE FIXED-POINT THEORY OF MULTI-VALUED MAPS § Multi-valued maps and single-valued approximations We denote by P{Y) the collection of all non-empty subsets of a set Y.

If Υ is a topological space, then C(Y) is the set of all its non-empty closed subsets, and K(Y) the set of all its non-empty compact subsets. If Υ is a subset of aCited by: We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.

Discover the world's research 16+ million membersAuthor: Vesko Valov. Preface.- Chapter I Background in Topology.- Chapter II Multivalued Mappings.- Chapter III Approximation Methods in Fixed Point Theory of Multivalued Mappings.- Chapter IV Homological Methods in Fixed Point Theory of Multivalued Mappings.- Chapter V Consequences and Applications.- Chapter VI Fixed Point Theory Approach to Differental Inclusions Lech Górniewicz, Homological methods in fixed-point theory of multi-valued maps, Dissertationes Math.

(Rozprawy Mat.) (), MR ; Lech Górniewicz and Andrzej Granas, Some general theorems in coincidence theory. I, J. Math. Pures Appl.

Homological methods in commutative algebra (Mathematical pamphlets - Tata Institute of Fundamental Research ; 5) Paperback – January 1, by S Raghavan (Author) › Visit Amazon's S Raghavan Page. Find all the books, read about the author, and more. Author: S Raghavan.Obstruction theory and single-valued approximations of multi-valued maps § Guide to the literature in Chapter I Chapter II.

Homological methods in the fixed-point theory of multi-valued maps.FIXED POINT THEORY FOR SET VALUED MAPS | Fixed point theory is an active area of research with wide range of applications in various directions. It is concerned with the results which state that.