Category: Topology

Category: Topology

Topology and Maps by Taqdir Husain (auth.)

By Taqdir Husain (auth.)

This paintings is acceptable for undergraduate scholars in addition to complicated scholars and learn staff. It involves ten chapters, the 1st six of that are intended for rookies and are for that reason compatible for undergraduate scholars; Chapters VII-X are compatible for complex scholars and study staff drawn to sensible research. This booklet has designated good points: First, it includes generalizations of continuing maps on topological areas, e. g. , nearly non-stop maps, approximately non-stop maps, maps with closed graph, graphically non-stop maps, w-continuous maps, and a-continuous maps, and so on. and a few in their homes. The remedy of those notions seems the following, in bankruptcy VII, for the 1st time in booklet shape. the second one characteristic is composed in a few not-so-easily-available nuptial delights that grew out of the wedding of topology and useful research; they're themes normally courted by way of practical analysts and infrequently given in topology books. in particular, one is familiar with that the set C(X) of all genuine- or com­ plex-valued non-stop features on a totally normal area X varieties a in the neighborhood convex topological algebra, a fortiori a topological vector house, within the compact-open topology. a couple of theorems are identified: for instance, C(X) is a Banach house iff X is compact, or C(X) is whole iff X is a kr-space, and so forth. Chapters VIII and X comprise this fabric, which, to the remorse of many readers has now not formerly been to be had in ebook shape (a fresh book (Weir [\06]) does, although, include a few fabric of our bankruptcy X).

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Category: Topology

Lectures on Three-Manifold Topology by William Jaco

By William Jaco

This manuscript is a close presentation of the 10 lectures given through the writer on the NSF neighborhood convention on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and country college. the aim of the convention used to be to give the present situation in three-manifold topology and to combine the classical effects with the numerous contemporary advances and new instructions.

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Category: Topology

Category: Topology

Introduction to Topology (2nd Edition) (Dover Books on by Theodore W. Gamelin, Robert Everist Greene

By Theodore W. Gamelin, Robert Everist Greene

This quantity explains nontrivial functions of metric area topology to research, in actual fact constructing their courting. additionally, themes from straightforward algebraic topology concentrate on concrete effects with minimum algebraic formalism. chapters reflect on metric area and point-set topology; the different 2 chapters discuss algebraic topological material. Includes routines, chosen solutions, and fifty one illustrations. 1983 version.

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Category: Topology

Quasiconformal Teichmuller Theory by Frederick P. Gardiner

By Frederick P. Gardiner

The Teichmuller house $T(X)$ is the distance of marked conformal buildings on a given quasiconformal floor $X$. This quantity makes use of quasiconformal mapping to offer a unified and up to date therapy of $T(X)$. Emphasis is put on elements of the idea appropriate to noncompact surfaces and to surfaces very likely of countless analytic variety. The ebook presents a remedy of deformations of advanced buildings on countless Riemann surfaces and provides heritage for extra examine in lots of components. those contain purposes to fractal geometry, to 3-dimensional manifolds via its courting to Kleinian teams, and to one-dimensional dynamics via its dating to quasisymmetric mappings. Many examine difficulties within the program of functionality idea to geometry and dynamics are steered.

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Category: Topology

Cohomological Methods in Transformation Groups by Christopher Allday, Volker Puppe

By Christopher Allday, Volker Puppe

Within the huge and thriving box of compact transformation teams a major position has lengthy been performed by way of cohomological equipment. This e-book goals to provide a modern account of such tools, particularly the purposes of normal cohomology conception and rational homotopy thought with central emphasis on activities of tori and uncomplicated abelian p-groups on finite-dimensional areas. for instance, spectral sequences aren't utilized in bankruptcy 1, the place the technique is via cochain complexes; and masses of the elemental idea of cochain complexes wanted for this bankruptcy is printed in an appendix. For simplicity, emphasis is wear G-CW-complexes; the refinements had to deal with extra basic finite-dimensional (or finitistic) G-spaces are frequently mentioned individually. next chapters supply systematic remedies of the Localization Theorem, functions of rational homotopy conception, equivariant Tate cohomology and activities on Poincaré duality areas. Many shorter and extra really expert subject matters are incorporated additionally. bankruptcy 2 includes a precis of the most definitions and effects from Sullivan's model of rational homotopy idea that are utilized in the e-book.

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Category: Topology

Knot Theory and Its Applications (Modern Birkhauser by Kunio Murasugi

By Kunio Murasugi

This booklet introduces the learn of knots, delivering insights into contemporary purposes in DNA study and graph conception. It units forth primary evidence corresponding to knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It additionally covers more moderen advancements and specific issues, comparable to chord diagrams and overlaying areas. the writer avoids complex mathematical terminology and complex suggestions in algebraic topology and workforce concept. quite a few diagrams and workouts support readers comprehend and practice the idea. every one bankruptcy incorporates a complement with attention-grabbing historic and mathematical reviews.

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Category: Topology

Category: Topology