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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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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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Statistical physics --- Geometry --- 536.75 --- Entropy. Statistical thermodynamics. Irreversible processes --- 536.75 Entropy. Statistical thermodynamics. Irreversible processes --- Fractals --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Fractals.
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Differential geometry. Global analysis --- Fractals --- Fractales --- Fractals. --- 517.542 --- #WPLT:dd.Prof.F.Symons --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Mappings of special domains --- 517.542 Mappings of special domains
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Differential equations --- Differential equations, Partial --- Équations aux dérivées partielles --- Spectral theory (Mathematics) --- Théorie spectrale (mathématiques) --- Functions, Zeta. --- Fonctions zêta. --- Fractals. --- Fractales. --- Numerical solutions. --- Solutions numériques. --- Fractals --- Functions, Zeta --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Zeta functions --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Numerical analysis --- Numerical solutions --- Solutions numériques
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Differential geometry. Global analysis --- Fractals --- Fractales --- Fractals. --- 517.987 --- #WBIB:dd.Lic.L.De Busschere --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology)
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Matter physics --- Differential geometry. Global analysis --- Statistical physics --- Stochastic processes --- Mathematical physics --- Analytical topology --- Fractals --- #TELE:SISTA --- 517.987 --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- geometry --- fractals --- Fractals.
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Algebraic topology --- Topology --- Dimension theory (Topology) --- Infinite dimensional manifolds. --- 515.127.1 --- Infinite dimensional manifolds --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Manifolds, Infinite-dimensional --- Global analysis (Mathematics) --- Topological manifolds --- Dimension theory --- 515.127.1 Dimension theory --- Topologie. --- Topology. --- Retracts, Theory of --- Rétractes, Théorie des --- Rétractes, Théorie des. --- Topologie --- Point fixe, Théorème du --- Topologie combinatoire
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Statistical physics --- Differential geometry. Global analysis --- Fractales --- Fractals --- 517.987 --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems
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Fractals --- Fractales --- 517.987 --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Fractals. --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Geometry --- BASIC (Computer program language) --- Infographie
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