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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.

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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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This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.

Topological dynamics. --- Dimension theory (Topology) --- Topology --- Dynamics, Topological --- Differentiable dynamical systems

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

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Dimension theory

Analytical topology --- Dimension theory (Topology) --- Metric spaces. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Topologie generale --- Dimension