Revision #600 → #1403 · back to history
addedMetric spacea87c2baa0cba
addedIdentity of indiscernibles axiomed668fd3b419
addedPositivity axiom4d007cf87e1e
addedSymmetry axiom9d3c68ab3a6e
addedTriangle inequality axiomd2646e3667c8
addedReal line as metric space9034f19fb0d1
addedEuclidean distancee116daef0ec8
addedTaxicab/Manhattan distance81939607b1d8
addedChebyshev distance761b1b285cb4
addedEquivalence of Euclidean, taxicab, Chebyshev metrics52377bac7858
addedDiscrete metric84b723d003c8
addedInduced metric on a subspaceb956c2633d72
addedOpen ballbf5d737bc3f8
addedNeighborhood06ae0d4402b7
addedOpen set1c9f127dea77
addedOpen balls form a base for a topologyeff3dabcc20c
addedMetrizable spacee78719d21751
addedNagata–Smirnov metrization theoreme7a74f4930df
addedConvergence in Euclidean space7eada1accc86
addedConvergence in a topological space8716903a4c2b
addedCauchy sequence94c95f50814b
addedConvergent sequences are Cauchyfce8f50633a5
addedComplete metric space6ef6e4f6a647
addedCompletion6588adbaf4ee
addedBounded metric spacee0a98643ab18
addedDiameter353ea8ce7aa8
addedTotally bounded spacefdca30a99ffb
addedTotally bounded implies boundede1a31c84fd44
addedCompact metric space (equivalent definitions)8f6e0a82266d
addedClosed interval is compact184c7c1f8f46
addedLebesgue's number lemmacccbee0ab432
addedDistance-preserving function43906c6b74d4
addedDistance-preserving functions are injectivea7fb2e8aac0e
addedIsometry2ec20186ae6b
addedIsometric spaces2a3fcbcde46b
addedContinuous map (topological)083f33c9f16a
addedSequential continuity6f4c3a827358
addedε–δ continuity5d2aff724463
addedHomeomorphism2cdbe417bf3a
addedUniformly continuous mapda24d2c8178c
addedUniformly continuous maps preserve Cauchy sequencesa8d9f7a511f3
addedHeine–Cantor theoremf9152cc803d7
addedLipschitz map84e3b76a4051
addedRectifiable iff has Lipschitz reparametrizationd70a87e68481
addedMetric map (nonexpanding)4d3098d99cf3
addedContractionbf31aa1a3fa0
addedBanach fixed-point theorem1f62862b0d3c
addedQuasi-isometric embeddingf81c9019484c
addedQuasi-isometry9b99efd589c8
addedŠvarc–Milnor lemmaf709a09a6c54
addedTopologically equivalent spaces00c1f41a8923
addedUniformic spacesbca872e73b74
addedBilipschitz homeomorphic0dba681bec51
addedQuasi-isometric spacesee9a345cae93
addedMetric induced by a normc6baa2d346ff
addedTranslation-invariant and homogeneous metric comes from a norm3604c7e6f7ea
addedBanach spaceee24bb86afcc
addedLinear maps continuous iff Lipschitzfac4f2e0d436
addedCurve and its lengtha2b9b048fe8b
addedRectifiable curvea85bb65d4818
addedGeodesic31b417f3247c
addedGeodesic metric space737c29270f63
addedLength space (intrinsic metric)a161a105fed1
addedPunctured plane is length but not geodesic5661b13a591c
addedSphere with straight-line metric not a length space478ea5067799
addedIntrinsic distance functionf212c265c1b8
addedRiemannian manifold and length of a pathcb66d77c1e2a
addedCAT(k) characterization of sectional curvature bound3940488e0dd7
addedMetric measure space3c1abcbf303d
addedDiscrete metric space383e7f26d5b3
addedGraph (shortest-path) metricdbc7ef12fb49
addedWord metricc238cf6888f1
addedProbabilistic embedding into tree metricf93052edacb2
addedUniform (supremum) metric on bounded functionsdf681d385546
addedCompleteness of bounded function spacec349834d4231
addedDistance from a point to a setccf16b38c8c6
addedDistance zero iff in closure4f02fa066a13
addedContinuity of distance-to-setbf5942ad5938
addedMetric spaces are completely regularf2618b6f243a
addedHausdorff distancee65f89f9e977
addedHausdorff distance is a metric on compact subsets0cedd3e46c10
addedGromov–Hausdorff distanceb5695208f9be
addedSnowflake of a metric1b57c218abe6
addedTight span52730a1a481c
addedKnight's move metric7f01be002b60
addedBritish Rail metric699b27fbf238
addedProduct metric8ce67cf7c1ad
addedCountable product metric59fc886a3aff
addedUncountable products need not be metrizablef5c79dcd0b5b
addedQuotient pseudometricc6452752cd44
addedUniversal property of quotient metric974284c7c230
addedSequential iff quotient of a metric spacea261ae4bb27f
addedExtended metric16c5023e9496
addedExtended metric replaceable by topologically equivalent real-valued metric9b761a713d04
addedPseudometricf5cdafed3667
addedQuasimetrica0e0b6fabc1c
addedQuasimetric on the reals19677bcc0e25
addedMetametric7ee1758fc9d1
addedSemimetricb3ef50bfe87e
addedρ-relaxed triangle and ρ-inframetric inequality55cd9c655a04
addedImplications between inframetric inequalitiesc3ccea0c7c29
addedPremetrica9597b5488b7
addedPremetric induces a topology99240b7f101a
addedPremetric space is sequential25af476a50f8
addedPseudoquasimetric (hemimetric)9af1deb2c98b
addedSierpiński space as pseudoquasimetric7be0bbedc31c
addedMetric on multisets4108ada26f95
addedMultiset metric restricts to ordinary metric42fbf8c8206e