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- In [[mathematics]], a '''complete metric space''' is a [[metric space]] in which every [[Cauchy sequence]] in that space i ...y metric space ''X'' has a '''completion''' <math>\bar X</math> which is a complete metric space in which ''X'' is [[isometry|isometrically]] embedded as a [[Denseness|dens3 KB (441 words) - 12:23, 4 January 2009
- 12 bytes (1 word) - 12:20, 4 January 2009
- 123 bytes (18 words) - 12:20, 4 January 2009
- 699 bytes (87 words) - 12:20, 4 January 2009
- 297 bytes (43 words) - 12:20, 4 January 2009
Page text matches
- A complete metric space in which a given metric space is isometrically embedded as a dense subspace136 bytes (20 words) - 07:38, 4 January 2009
- ...ry, equivalently, the intersection of any sequence of open dense sets in a complete metric space is dense.199 bytes (30 words) - 06:18, 4 September 2009
- * A discrete metric space is [[complete metric space|complete]]456 bytes (71 words) - 12:47, 4 January 2009
- #REDIRECT [[Complete metric space#Topologically complete space]]64 bytes (7 words) - 12:42, 4 January 2009
- In [[mathematics]], a '''complete metric space''' is a [[metric space]] in which every [[Cauchy sequence]] in that space i ...y metric space ''X'' has a '''completion''' <math>\bar X</math> which is a complete metric space in which ''X'' is [[isometry|isometrically]] embedded as a [[Denseness|dens3 KB (441 words) - 12:23, 4 January 2009
- * [[Complete metric space]]120 bytes (13 words) - 12:25, 4 January 2009
- {{r|Complete metric space}}942 bytes (125 words) - 18:29, 11 January 2010
- #REDIRECT [[Complete metric space/Bibliography]]48 bytes (5 words) - 12:20, 4 January 2009
- #REDIRECT [[Complete metric space/Related Articles]]52 bytes (6 words) - 12:20, 4 January 2009
- {{r|Complete metric space}}423 bytes (60 words) - 15:14, 28 July 2009
- ...e>A theorem that states the existence and uniqueness of a fixed-point in a complete metric space.130 bytes (19 words) - 05:07, 16 January 2012
- * A subset of a [[complete metric space]] is totally bounded if and only if its [[closure (topology)|closure]] is [975 bytes (166 words) - 15:27, 6 January 2009
- The ''p''-adic metric on '''Q''' is not [[complete metric space|complete]]: the [[p-adic number]]s are the corresponding [[completion]].1 KB (168 words) - 12:39, 4 January 2009
- * A G<sub>δ</sub> in a [[complete metric space]] is again a complete metric space.1 KB (223 words) - 13:16, 8 March 2009
- *[[Complete metric space]]389 bytes (39 words) - 12:37, 4 January 2009
- The Cantor set is a [[complete metric space]] with respect to ''d''.2 KB (306 words) - 16:51, 31 January 2011
- ...uchy sequences may be convergent or not. This leads to the notion of a ''[[complete metric space]]'' as one in which every Cauchy sequence converges to a point of the space1 KB (240 words) - 12:30, 4 January 2009
- ...the branch known as [[functional analysis]], a '''Hilbert space''' is a [[complete metric space|complete]] [[inner product space]]. As such, it is automatically also a [[B2 KB (258 words) - 12:33, 4 January 2009
- ...category'''. The ''[[Baire category theorem]]'' states that a non-empty [[complete metric space]] is of second category.850 bytes (118 words) - 22:30, 20 February 2010
- ..., the '''Baire category theorem''' states that a non-[[empty set|empty]] [[complete metric space]] is a [[second category space]]: that is, it is not a [[countability|count501 bytes (67 words) - 23:00, 5 February 2009
- {{r|Complete metric space}}566 bytes (74 words) - 16:25, 11 January 2010
- {{r|Complete metric space}}689 bytes (88 words) - 17:15, 11 January 2010
- {{r|Complete metric space}}241 bytes (34 words) - 12:31, 4 January 2009
- {{r|Complete metric space}}940 bytes (149 words) - 15:13, 28 July 2009
- {{r|Complete metric space}}955 bytes (150 words) - 15:15, 28 July 2009
- {{r|Complete metric space}}462 bytes (60 words) - 16:44, 11 January 2010
- {{r|Complete metric space}}681 bytes (91 words) - 18:06, 11 January 2010
- ...the '''Banach's fixed-point theorem''' states that a contracting map in a complete metric space has a unique fixed-point. Given a complete metric space (''X'',''ρ''), i.e. a metric space in which every [[Cauchy sequence]] {''x6 KB (996 words) - 06:49, 16 January 2012
- ...sconnected]]. The rational numbers do not form a [[completeness (topology)|complete metric space]]; the [[real numbers]] are the completion of <math>\mathbb{Q}</math>.9 KB (1,446 words) - 08:52, 30 May 2009
- Every Euclidean space is also a complete metric space. Moreover, all geometric notions immanent to a Euclidean space can be chara28 KB (4,311 words) - 08:36, 14 October 2010
- ...ch that <math>c_1\rho(x,y)\le\rho(f(x),f(y))\le c_2\rho(x,y)</math> from a complete metric space (''X'',''ρ''), the dimension is preserved, because the inverse map is also15 KB (2,549 words) - 09:18, 17 February 2012
- ...es, the corresponding qualitative theory of the eigenfunctions and their [[Complete metric space|completeness]] in a suitable [[function space]] became known as '''Sturm–15 KB (2,332 words) - 04:52, 18 October 2009
- ...nce]]s. This notion has led to the fundamental mathematical concept of a [[complete metric space]]. The [[Cauchy condition]] for the convergence of [[series (mathematics)|s20 KB (3,286 words) - 12:52, 24 August 2013