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Embeddings (Mathematics) --- Manifolds (Mathematics)

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Topological embeddings

Algebraic topology --- Topological imbeddings. --- Topological imbeddings --- Embeddings, Topological --- Imbeddings, Topological --- Topological embeddings --- Embeddings (Mathematics) --- Variétés topologiques

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Concordances (Topology) --- Embeddings (Mathematics) --- Piecewise linear topology

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Toric varieties. --- Embeddings, Torus --- Torus embeddings --- Varieties, Toric --- Algebraic varieties --- Mathematics --- Algebra --- Geometry --- Toric varieties --- Geometrie algebrique --- Colloque --- Varietes algebriques

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This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.

Dimension theory (Topology) --- Attractors (Mathematics) --- Topological imbeddings. --- Embeddings, Topological --- Imbeddings, Topological --- Topological embeddings --- Embeddings (Mathematics) --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems --- Topology