Introduction to Topology: Pure and Applied by Colin Adams, Robert Franzosa

By Colin Adams, Robert Franzosa

Examine the fundamentals of point-set topology with the knowledge of its real-world software to quite a few different topics together with technological know-how, economics, engineering, and different components of mathematics.

Introduces topology as an enormous and engaging arithmetic self-discipline to hold the readers curiosity within the topic. Is written in an obtainable method for readers to appreciate the usefulness and significance of the appliance of topology to different fields. Introduces topology options mixed with their real-world program to topics such DNA, center stimulation, inhabitants modeling, cosmology, and special effects. Covers subject matters together with knot idea, measure thought, dynamical structures and chaos, graph concept, metric areas, connectedness, and compactness.

A worthy reference for readers short of an intuitive creation to topology.

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Sheaf Theory by Glen E. Bredon (auth.)

By Glen E. Bredon (auth.)

This e-book is essentially involved in the examine of cohomology theories of common topological areas with "general coefficient structures. " Sheaves play numerous roles during this research. for instance, they supply an appropriate proposal of "general coefficient structures. " in addition, they provide us with a standard approach to defining a number of cohomology theories and of comparability among various cohomology theories. The elements of the idea of sheaves lined listed here are these components impor­ tant to algebraic topology. Sheaf concept can also be vital in different fields of arithmetic, particularly algebraic geometry, yet that's outdoor the scope of the current ebook. hence a extra descriptive identify for this booklet could have been Algebraic Topology from the perspective of Sheaf concept. a number of techniques should be present in this e-book. significantly, the con­ cept of the "tautness" of a subspace (an edition of the same no­ tion of Spanier to sheaf-theoretic cohomology) is brought and exploited through the publication. the truth that sheaf-theoretic cohomology satisfies 1 the homotopy estate is proved for basic topological areas. additionally, relative cohomology is brought into sheaf conception. pertaining to relative cohomology, it's going to be famous that sheaf-theoretic cohomology is mostly regarded as a "single house" theory.

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A Course in Point Set Topology (Undergraduate Texts in by John B. Conway

By John B. Conway

This textbook in aspect set topology is geared toward an upper-undergraduate viewers. Its mild velocity may be important to scholars who're nonetheless studying to put in writing proofs. necessities comprise calculus and a minimum of one semester of research, the place the coed has been correctly uncovered to the information of simple set concept akin to subsets, unions, intersections, and capabilities, in addition to convergence and different topological notions within the actual line. Appendices are integrated to bridge the space among this new fabric and fabric present in an research path. Metric areas are one of many extra ordinary topological areas utilized in different components and are as a result brought within the first bankruptcy and emphasised through the textual content. This additionally conforms to the procedure of the e-book to begin with the actual and paintings towards the extra normal. bankruptcy 2 defines and develops summary topological areas, with metric areas because the resource of idea, and with a spotlight on Hausdorff areas. the ultimate bankruptcy concentrates on non-stop real-valued features, culminating in a improvement of paracompact areas.

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Topology in Process Calculus: Approximate Correctness and by Mingsheng Ying

By Mingsheng Ying

Communication and concurrency are crucial in figuring out complicated dynamic platforms, and there were many theories to house them comparable to Petri nets, CSP and ACP. between them, CCS (process calculus is likely one of the most vital and mathematically built versions of conversation and concurrency. quite a few habit equivalences among brokers, reminiscent of (strong and vulnerable) bisimilarity, commentary congruence, hint equivalence, checking out equivalence and failure equivalence, are primary notions in approach calculus. within the actual functions of technique calculus, specification and implementation are defined as brokers, correctness of courses is taken care of as a definite habit equivalence among specification and implementation, after which the facts of correctness of courses is a role to set up a few habit equivalence among them. The objective of this publication is to supply a few appropriate and beneficial techniques and instruments for the knowledge and research of approximate correctness of courses in concurrent platforms. all through this publication the focal point is at the framework of approach calculus, and the most thought is to build a few traditional and moderate topological buildings which could show certainly a mechanism of approximate computation in strategy calculus and to see quite a few relationships between procedures which have compatibility with those topological structures.

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Topologie by Klaus Jänich

By Klaus Jänich

Aus den Rezensionen: "Was das Buch vor allem auszeichnet, ist die unkonventionelle Darstellungsweise. Hier wird Mathematik nicht im trockenen Definition-Satz-Beweis-Stil geboten, sondern sie wird dem Leser pointiert und mit viel Humor schmackhaft gemacht. In ungewöhnlich fesselnder Sprache geschrieben, ist die Lektüre dieses Buches auch ein belletristisches Vergnügen. speedy 2 hundred sehr instruktive und schöne Zeichnungen unterstützen das Verständnis, motivieren die behandelten Aussagen, modellieren die tragenden Beweisideen heraus. Ungewöhnlich ist auch das sign in, das unter jedem Stichwort eine Kurzdefinition enthält und somit umständliches Nachschlagen erspart". Wiss. Zeitschrift der TU Dresden

Jetzt in der achten Auflage des bewährten Lehrbuches!

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Algebraic Topology (Colloquium Publications, Volume 27) by Solomon Lefschetz

By Solomon Lefschetz

Because the booklet of Lefschetz's Topology (Amer. Math. Soc. Colloquium courses, vol. 12, 1930; spoke of under as (L)) 3 significant advances have stimulated algebraic topology: the improvement of an summary advanced self reliant of the geometric simplex, the Pontrjagin duality theorem for abelian topological teams, and the strategy of Cech for treating the homology concept of topological areas via structures of "nerves" every one of that's an summary complicated. the result of (L), very materially further to either by way of incorporation of next released paintings and by way of new theorems of the author's, are the following thoroughly recast and unified when it comes to those new ideas. A excessive measure of generality is postulated from the outset.

The summary perspective with its concomitant formalism allows succinct, unique presentation of definitions and proofs. Examples are sparingly given, typically of an easy variety, which, as they don't partake of the scope of the corresponding textual content, may be intelligible to an user-friendly pupil. yet this is often essentially a e-book for the mature reader, during which he can locate the theorems of algebraic topology welded right into a logically coherent complete

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The User's Approach to Topological Methods in 3D Dynamical by Maro A. Natiello, Hernán G Solari

By Maro A. Natiello, Hernán G Solari

This booklet provides the improvement and alertness of a few topological equipment within the research of information coming from 3D dynamical structures (or similar objects). the purpose is to stress the scope and barriers of the equipment, what they supply and what they don't offer. Braid concept, the topology of floor homeomorphisms, information research and the reconstruction of phase-space dynamics are completely addressed.

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Dynamical Systems: An Introduction (Universitext) by Luis Barreira, Claudia Valls

By Luis Barreira, Claudia Valls

The idea of dynamical structures is a large and lively study topic with connections to such a lot elements of arithmetic. Dynamical structures: An advent undertakes the tough job to supply a self-contained and compact introduction.

Topics coated contain topological, low-dimensional, hyperbolic and symbolic dynamics, in addition to a short creation to ergodic idea. specifically, the authors contemplate topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson thought, and the development of reliable manifolds, in addition to an creation to geodesic flows and the research of hyperbolicity (the latter is frequently absent in a primary introduction). in addition, the authors introduce the fundamentals of symbolic dynamics, the development of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.

The exposition is mathematically rigorous, concise and direct: all statements (except for a few effects from different parts) are confirmed. whilst, the textual content illustrates the speculation with many examples and a hundred and forty workouts of variable degrees of hassle. the one necessities are a history in linear algebra, research and hassle-free topology.

This is a textbook essentially designed for a one-semester or two-semesters path on the complex undergraduate or starting graduate degrees. it could even be used for self-study and as a kick off point for extra complex issues.

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