Results 311 to 317 of about 564,721 (317)
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2006
Publisher Summary This chapter provides an overview of the topological spaces. A topological space (X, τ) is a set X with a topology τ, that is, a collection of subsets of X with the following properties: (1) X ∈ τ, o ∈ τ; (2) if A, B ∈ τ then A ∩ B ∈ τ ; and (3) for any collection {Aα}α, if all Aα ∈ τ , then UαAα ∈ τ .
Elena Deza, Michel-Marie Deza
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Publisher Summary This chapter provides an overview of the topological spaces. A topological space (X, τ) is a set X with a topology τ, that is, a collection of subsets of X with the following properties: (1) X ∈ τ, o ∈ τ; (2) if A, B ∈ τ then A ∩ B ∈ τ ; and (3) for any collection {Aα}α, if all Aα ∈ τ , then UαAα ∈ τ .
Elena Deza, Michel-Marie Deza
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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.
Gerhard Rosenberger, Benjamin Fine
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Topological Vector Spaces [PDF]
, 1982 Vector spaces will be considered as vector spaces over ℂ unless something else is specified. The symbols Hom(X, Y) resp. Sur(X, Y) will be reserved for sets of continuous homomorphisms resp. surjective homomor-phisms; End(X) is the set of continuous endomorphisms and Aut(E) is the set of continuous automorphisms (bijective and bicontinuous ...
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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]
Herbert Edelsbrunner, Nimish R. Shah
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1966
Publisher Summary This chapter defines topological spaces and the related theorems. The condition for a set A to be open in a metric space is that each point of A belongs to an open ball contained in A. A space that contains no other closed-open subset is called connected. The union of two closed sets is a closed set.
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Publisher Summary This chapter defines topological spaces and the related theorems. The condition for a set A to be open in a metric space is that each point of A belongs to an open ball contained in A. A space that contains no other closed-open subset is called connected. The union of two closed sets is a closed set.
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