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Ordered Sets
Author: Bernd Schröder
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 401
ISBN-13: 1461200539
DOWNLOAD EBOOK →An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Algebraic Topology of Finite Topological Spaces and Applications
Author: Jonathan A. Barmak
Publisher: Springer
Published: 2011-08-24
Total Pages: 184
ISBN-13: 3642220037
DOWNLOAD EBOOK →This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
An Introduction to Partially Ordered Structures and Sheaves
Author: Francisco Miraglia
Publisher: Polimetrica s.a.s.
Published: 2006
Total Pages: 517
ISBN-13: 8876990356
DOWNLOAD EBOOK →Ordered Sets
Author: Bernd Schröder
Publisher: Birkhäuser
Published: 2016-05-11
Total Pages: 426
ISBN-13: 3319297880
DOWNLOAD EBOOK →An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Ordered Sets and Lattices II
Author:
Publisher: American Mathematical Soc.
Published:
Total Pages: 262
ISBN-13: 9780821895887
DOWNLOAD EBOOK →This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
Linear Representations of Partially Ordered Sets and Vector Space Categories
Author: Daniel Simson
Publisher: CRC Press
Published: 1993-01-01
Total Pages: 516
ISBN-13: 9782881248283
DOWNLOAD EBOOK →This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.
Algebraic Topology of Finite Topological Spaces and Applications
Author: Jonathan A. Barmak
Publisher: Springer Science & Business Media
Published: 2011-08-24
Total Pages: 184
ISBN-13: 3642220029
DOWNLOAD EBOOK →This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Ordered Sets
Author: Egbert Harzheim
Publisher: Springer Science & Business Media
Published: 2005-02-17
Total Pages: 391
ISBN-13: 0387242198
DOWNLOAD EBOOK →The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory.
Partially Ordered Algebraic Systems
Author: Laszlo Fuchs
Publisher: Courier Corporation
Published: 2014-03-05
Total Pages: 242
ISBN-13: 0486173607
DOWNLOAD EBOOK →This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.
