منابع مشابه
The Completion of a Metric Space
Let (X, d) be a metric space. The goal of these notes is to construct a complete metric space which contains X as a subspace and which is the “smallest” space with respect to these two properties. The resulting space will be denoted by X and will be called the completion of X with respect to d. The hard part is that we have nothing to work with except X itself, and somehow it seems we have to p...
متن کاملMetric Properties of Outer Space
We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmüller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metr...
متن کاملThe Completion of a Metric Space
C[E] := {a : (an)n∈N is a Cauchy sequence in (E, d)} . You should think of C[E] as a new space where each point a ∈ C[E] is a Cauchy sequence a = (an)n∈N from (E, d). Note that for each x ∈ E, we can define x ∈ C[E] by letting xn = x for all n ∈ N. This gives us a way to think of C[E] as containing our original space E, which we will make more precise in Section 3. For a, b ∈ C[E] we define D(a...
متن کاملOn the Yoneda completion of a quasi-metric space
Several theories aimed at reconciling the partial order and the metric space approaches to Domain Theory have been presented in the literature (e.g. Flagg and Kopperman, Theoret. Comput. Sci. 177 (1) (1997) 111–138; Bonsangue et al., Theoret. Comput. Sci. 193 (1998) 1–51; Symth, Quasi-Uniformities: Reconciling Domains with Metric Spaces, Lectures Notes in Computer Science, vol. 298, Springer, B...
متن کاملA double completion for an arbitrary T0-quasi-metric space
We present a conjugate invariant method for completing any T0-quasi-metric space. The completion is built as an extension of the bicompletion of the original space. For balanced T0-quasi-metric spaces our completion yields up to isometry the completion due to Doitchinov. The question which uniformly continuous maps between T0-quasimetric spaces can be extended to the constructed completions lea...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2019
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-019-00451-3