منابع مشابه
Geometry of Epimorphisms and Frames
Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(`2,H) of all (bounded linear) operators from `2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F . We show that each component is a homogeneous space of the group GL(`2) of invertible operators of `2. This geometric...
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A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is χ-bounded if there exists a function f : N → N such that for all graphs G ∈ G, and all induced subgraphs H of G, we have that χ(H) ≤ f(ω(H)). We prove that proper homogeneous sets, clique-cutsets, and amalgams together preserve χ-boundedness. More precisely, we show that if G and G∗ a...
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This paper studies the homomorphism of rings of continuous functions ρ:C(X) → C(Y ), Y a subspace of a Tychonoff space X, induced by restriction. We ask when ρ is an epimorphism in the categorical sense. There are several appropriate categories: we look at CR, all commutative rings, and R/N, all reduced commutative rings. When X is first countable and perfectly normal (e.g., a metric space), ρ ...
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We consider the relations ≥ and ≥p on the collection of all knots, where k ≥ k (respectively, k ≥p k) if there exists an epimorphism πk → πk of knot groups (respectively, preserving peripheral systems). When k is a torus knot, the relations coincide and k must also be a torus knot; we determine the knots k that can occur. If k is a 2-bridge knot and k ≥p k, then k is a 2-bridge knot with determ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1988
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-56-1-1-17