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A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces. It makes the subject accessible to beginning graduate students and will also serve as a reference work for general topologists. Two introductory chapters summarize standard results in general topology, and cover material on paracompactness and metrization. The principal definitions of dimension follow and their general properties are deduced. Many examples are analysed to show some of the more surprising or pathological aspects of dimension theory. Wherever it is useful to do so, proofs are given in detail.

Topology --- Dimension theory (Topology) --- Topological spaces. --- Dimension theory (Topology). --- Topologie generale --- Dimension

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Topology --- Topological spaces. --- Dimension theory (Topology) --- Dimension theory (Topology). --- Topological spaces --- Spaces, Topological --- 515.12 --- 515.12 General topology --- General topology

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Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a s

Dimension theory (Topology) --- Mappings (Mathematics) --- Compactifications. --- Topology --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Transformations (Mathematics)

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This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the bo

Fractals. --- Poincaré series. --- Series, Poincaré --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology)

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Fractals. --- Rock mechanics. --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Geotechnical engineering --- Mechanics