Completion of a Metric SpaceDefine, X
(Theoret. Comput. Sci. 193 (1998) 1–51): “An interesting question is to characterize the family of generalized metric spaces for which [the Yoneda] completion is idempotent (it contains at least all ordinary metric spaces)”. We show that the largest class of quasi-metric spaces ...
be introduced that has properties analogous to the properties of ordinary distance. The set is then said to be a metric space. The concept of the limit of a sequence of points in the metric space can be defined in the usual way. If the Cauchy criterion holds, the space is called ...
Cantor's famous construction of the real continuum in terms of Cauchy sequences of rationals proceeds by imposing a suitable equivalence relation. More generally, the completion of a metric space starts from an analogous equivalence relation among sequences of points of the space. Can Cantor's ...
For when a man has once undertaken a business, let him go through-stitch with it. (The Pagan Prince, 1690) in for a penny, in for a pound Once involved in a matter, however slightly, one must carry it through whatever the consequences. The metaphor comes from the monetary units of Gr...
a non-technical term used to describe the last stage of a sale of land when the land and its title are exchanged for the price. For Scotland, see SETTLEMENT. Collins Dictionary of Law © W.J. Stewart, 2006 Want to thank TFD for its existence? Tell a friend about us, add a link ...
Teichmüller spaceWeil–Petersson metricGiven a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmuller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric characteristics of the ...
(law) The conclusion of an act of conveyancing concerning the sale of a property. (mathematics) The act of making a metric space complete by adding points. (mathematics) The space resulting from such an act. noun The act or state of being or making something complete; conclusion, acc...
mathematics: act of making a metric space complete by adding points [..] en.wiktionary.org_2014 完成 noun (be) finished It is a basic quality of an employee to complete his tasks within a fixed time. 在限定时间内完成任务是一个职员的基本素质。 English Taiwanese Dictionary 竣工 ve...
We summarize some recent results showing how the lambdacalculus may be obtained by considering the metric completion (with respect to a suitable notion of distance) of a space of affine lambda-terms, i.e., lambda-terms in which abstractions bind variables appearing at most once. This formalizes...