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Triangulating topological spaces
Proceedings of the tenth annual symposium on Computational geometry - SCG '94, 1994Given a subspace [Formula: see text] and a finite set S⊆ℝd, we introduce the Delaunay complex, [Formula: see text], restricted by [Formula: see text]. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets [Formula: see text] in a non-empty set. By the nerve theorem, [Formula: see text] and [Formula: see text]
Edelsbrunner, Herbert, Shah, Nimish R.
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Ultracomplete Topological Spaces
Acta Mathematica Hungarica, 2001If \(X\) is a set and \(\Sigma\) is a set of coverings of \(X\), then we can consider \((X,\Sigma)\) to be a generalized uniform space. This point of view originates from the work of \textit{J. W. Tukey} [Convergence and uniformity in topology, Princeton (1940)] who used \((X,\Sigma)\), where \(\Sigma\) fulfills some appropriate conditions, as another ...
Buhagiar, D., Yoshioka, I.
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advg, 2005
Abstract Two of the problems listed in [14, 74.17] ask to prove or disprove the following statements: A) For each differentiable planar map ƒ : IR2 → IR2 the set of all differentials defines a ...
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Abstract Two of the problems listed in [14, 74.17] ask to prove or disprove the following statements: A) For each differentiable planar map ƒ : IR2 → IR2 the set of all differentials defines a ...
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Topology and Topological Spaces
1997We have now seen four different proofs of the Fundamental Theorem of Algebra. The first two were purely analysis, while the second pair involved a wide collection of algebraic ideas. However, we should realize that even in these algebraic proofs we did not totally leave analysis.
Benjamin Fine, Gerhard Rosenberger
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1994
Abstract The purpose of this chapter is to provide the theoretical background for a rigorous discussion of knots and surfaces, against which the vaguely expressed ideas lying behind our previous discussion can be made precise. The central notion is that of a topological space.
N D Gilbert, T Porter
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Abstract The purpose of this chapter is to provide the theoretical background for a rigorous discussion of knots and surfaces, against which the vaguely expressed ideas lying behind our previous discussion can be made precise. The central notion is that of a topological space.
N D Gilbert, T Porter
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General Topology Topological Spaces
1987The purpose of this chapter is to present very rapidly some of the basic, concise results in general topology – mostly without proofs. The reader interested in this topic may consult the works of N. Bourbaki, J. L. Kelley and K. Kuratowski for a detailed account.
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1992
In terms of neighborhood filters with bases composed of open sets, closed sets, regular-open sets or regular-closed sets and the intersection of these filters, the authors define separation type properties \(M_ 1\), \(M_ 2\), \(M_{2.5}\), \(M_ 3\), as well as some strong or weak variations, in terms of the intersection of these filters.
LO FARO, Giovanni, Santoro G.
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In terms of neighborhood filters with bases composed of open sets, closed sets, regular-open sets or regular-closed sets and the intersection of these filters, the authors define separation type properties \(M_ 1\), \(M_ 2\), \(M_{2.5}\), \(M_ 3\), as well as some strong or weak variations, in terms of the intersection of these filters.
LO FARO, Giovanni, Santoro G.
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