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Soft cover. Condizione: 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-dimensiona…l manifolds. 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.
