Zarichnyi michael (3 Ergebnisse)
- Softcover
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Soft cover. Zustand: New. 8vo (21.5 cm), 263 pp. Publisher's laminated wrappers. Mathematical Studies: Monograph Series, vol. 5. A research monograph in categorical and general topology by Andrij Teleiko (Ternopil Academy of Economics) and Michael Zarichnyi (Lviv National University), presenting a systematic treatment of normal…functors in the category of compact Hausdorff spaces. Building upon the foundational work of Evgenii Shchepin, the authors develop a unified theory for a class of functors broad enough to encompass many of the principal constructions of modern topology--including hyperspaces, spaces of probability measures, inclusion hyperspaces, superextensions, and related functorial constructions--while sufficiently restrictive to admit a rich general theory. The volume substantially expands Zarichnyi's earlier Ukrainian-language monograph of 1993. The five chapters comprise: Preliminaries, introducing the necessary background in general topology (including the Shchepin spectral theorem, dimension theory, and Milutin maps) and category theory (monads, Eilenberg-Moore and Kleisli categories, and extensions of contravariant functors); Normal Functors, discussing numerous examples before developing the general theory of normal functors, supports, finite-degree functors, extensions to Tychonoff spaces, extension operators, multiplicativity, openness, bicommutativity, and characterizations of normality; Normal Monads, treating the power, hyperspace, inclusion hyperspace, and probability-measure monads, tensor products, distributive laws, Kleisli categories, Eilenberg-Moore algebras, liftings of functors, and perfectly metrizable monads, including the fractal objects they generate; Geometric Properties of Functors, examining the preservation of finite-dimensional manifolds, ANR- and LCⁿ-spaces, equivariant Hilbert cubes, and shape-theoretic and homotopy properties; and Functors and Nonmetrizable Compacta, devoted to hyperspaces and probability-measure spaces of nonmetrizable compacta, homeomorphism problems for uncountable functor powers, and related questions in infinite-dimensional topology. As the authors note in the preface, the final chapters are intended to illustrate the interaction of categorical topology with geometric topology, absolute extensors, infinite-dimensional manifolds, and equivariant topology rather than to provide a fully self-contained treatment. An important contribution to modern categorical topology, serving both as a comprehensive reference on normal functors and as a guide to their applications in infinite-dimensional and nonmetrizable topology.
- Softcover
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EUR 34,62
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Soft cover. Zustand: New. 8vo (21.5 cm), 232 pp. Publisher's laminated wrappers. Mathematical Studies: Monograph Series, vol. 1. A research monograph in infinite-dimensional topology presenting a systematic, self-contained account of the theory of absorbing sets--one of the central tools in the topology of infinite-dimensional m…anifolds. The authors trace the subject from Anderson's cap-sets, Bessaga-Pełczyński's skeletoids, and J. West's absorbing sets, through Henryk Toruńczyk's landmark characterization theorems for Hilbert space and Hilbert cube manifolds of the early 1970s, to the modern framework established by M. Bestvina and J. Mogilski. Departing from the Bestvina-Mogilski approach, the authors develop the theory from the first author's characterization of spaces admitting homotopy-dense embeddings into Hilbert space manifolds, yielding a more streamlined exposition while establishing the equivalence of the relative (Bestvina-Mogilski) and absolute (Dobrowolski-Mogilski) notions of absorbing sets, the latter being termed absorbing spaces throughout the volume. The five chapters treat: Basic Theory (homotopy-dense and homotopy-negligible sets, the strong discrete approximation property, Z-sets, strong universality, absorbing and coabsorbing spaces, and absorbing pairs); Constructions of Absorbing Spaces (descriptive set theory, dimension theory, invertible and soft maps, weak inverse limits, and absorbing spaces for [0,1]-stable classes); Advanced Topics (the relationship between strongly universal spaces and pairs, together with characterizations of strong C-universality); Applications I (infinite products, topological groups, and hyperspaces); and Applications II: Convex Sets (locally compact and topologically complete convex sets, strong universality in convex and locally convex spaces, counterexamples, spaces of probability measures, and the function spaces Cₚ(X) and Cₚ*(X)). An important contribution to modern infinite-dimensional topology, intended for researchers and graduate students working in geometric topology, infinite-dimensional manifolds, and topological algebra.
- Hardcover
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Hardcover. Zustand: New. 8vo (21.5 cm), 219 pp. Publisher's laminated boards. Mathematical Studies: Monograph Series, vol. 12. Edited by Michael Zarichnyi. A research monograph in large-scale and asymptotic geometry by Ihor Protasov (Kyiv University) and Michael Zarichnyi (Lviv University and University of Rzeszów), developing t…he theory of ball structures and balleans as a combinatorial and set-theoretic framework for large-scale geometry. Independently developed by Protasov in connection with problems concerning partitions of groups, the theory provides a common language for phenomena appearing in Gromov's large-scale geometry, Roe's coarse structures, and asymptotic dimension theory. As the authors explain in the preface, the book deliberately alternates between the "micro" language of ball structures and the "macro" language of coarse structures, regarding the two viewpoints as complementary descriptions of the same large-scale phenomena. The ten chapters cover ball structures and balleans, their mappings and the coarse category; metrizability and approximation; cellularity and pseudodiscreteness, including connections with asymptotic dimension zero and non-Archimedean and ultrametric spaces; normality and asymptotic separation; graph balleans, including monogenic balleans, the Gromov product, coarse trees, and coarse rays; group balleans, with group ideals, countable and Abelian groups, and ultrafilters; asymptotic oscillations and slowly oscillating functions; coronas, including the Higson corona; cardinal invariants such as density, capacity, resolvability, and coresolvability; and maximal balleans. Numerous examples and exercises accompany the chapters. The introduction places the theory in the development of modern coarse geometry, from Gromov's asymptotic dimension and its applications by G. Yu to the Novikov Higher Signature conjecture, through Dranishnikov's work relating asymptotic invariants to Higson coronas, to Roe's axiomatization of coarse structures. Conceived as a development and complement to Roe's foundational treatment, and as a continuation of the authors' Ball Structures and Colorings of Graphs and Groups (2003), this volume extends their ball-structure formalism into a systematic theory of coarse and asymptotic geometry. An important reference for researchers in geometric group theory, coarse topology, and large-scale geometry.
