Revision #510 → #1098 · back to history
addedExtreme value theorem (Euclidean)491e48d787e0
addedCompact topological space (open cover)5eec12fa9bf3
addedHeine–Borel theorem (lead)204e0f88f209
addedCompact set (terminology)c53ab9b25a4f
addedBolzano's theorem on limit points645e70946b47
addedArzelà–Ascoli theorem (historical)1cab82d46779
addedHeine's uniform continuity theoremd0efbd548fdd
addedHeine–Borel lemmad772338dfef8
addedUnit interval is compactc35bbc2e9c6a
addedHalf-line [0,∞) not compact5c9f3009ea62
addedClosed disks and circles compact; open disk not38272fc62789
addedSpheres compact; punctured sphere not; lines/planes not01ca6dca724e
addedCompactness in Euclidean spacea0bc97788b41
addedBicompactness / open cover definition9d08db144052
addedCompact topological space (formal)523941b20cc5
addedQuasi-compact and compactumcd3a362f8ec7
addedCompact subset2ab538ce9ddf
addedCompactness via subspace topology8ff87b8e4e98
addedCharacterizations of compactnessad8608cfd0f8
addedBourbaki's definition of compact space095a0a30bcdc
addedHeine–Borel theorem84c6c900df21
addedEquivalent compactness conditions for metric spacesb4d3db57ac84
addedLebesgue's number lemmadb3d82e9871c
addedCompact metric space is second-countable, separable, Lindelöfc1badaa52f91
addedCompact metric subset is closed and bounded075d906d8b2e
addedEquivalent compactness conditions for ordered spaces0510d924fe65
addedComplete lattice7bdbc5b5c7f8
addedSequential properties of compact ordered spaces82f6e6b9ff59
addedEvaluation map is a ring homomorphism3add53ccfb9b
addedPseudocompactness and realcompactness via maximal ideals6400bb805586
addedNon-standard characterization of compactness5bbe55e41bb7
addedHyperreal definition of compactnessc37bf746029a
addedOpen interval not compact via hyperrealsfee20ca990e4
addedClosed subset of compact space is compacta0bc75d63644
addedFinite union of compact sets is compact6bc38e22655a
addedContinuous image of compact space is compact3bd9e6b11195
addedIntersection of compact subsets of Hausdorff spacea3bd24a68068
addedTychonoff's theorem29cb92d6e0ac
addedCompact iff sequentially compact in metrizable space20f0ea7bcc73
addedFinite set is compact07e7f4d7c00b
addedKC spaceb9aa6375c393
addedCompact subset of Hausdorff space is closed4e0e7244ea9e
addedCompact subset of TVS is complete0fcfa5b1cac2
addedSeparation of disjoint compacts in Hausdorff space03c95785588c
addedContinuous bijection from compact to Hausdorff is homeomorphismca21facfd6e3
addedCompact Hausdorff is normal and regularef9158bf04d2
addedCompact Hausdorff topology extremalitydadf43a75ccd
addedCompact metric subset is bounded4ccdd85649f0
addedExtreme value theoremf242c610af5c
addedPre-image under proper map is compactdd4a99733048
addedAlexandroff one-point compactification55dfe8dc9327
addedCompact subset of reals has max and min5eb78b711620
addedCompact ordered space iff complete lattice2fe9def85647
addedFinite topological space is compacte8c3d710572a
addedCofinite topology is compact869e3a685b3f
addedAlexandroff compactification examples767634c86f61
addedOrder topology on bounded totally ordered set compact1d3358326df5
addedDiscrete spaces and compactness134dcbb63300
addedLower limit topology uncountable not compacte2465a8e385c
addedCocountable topology infinite not compact61af29d25705
added[0,1] compact, (0,1) not, rationals in [0,1] not4657a8e5fb6f
addedReal line not compactbf2136bad1e5
addedExtended real line is compactd825f918f16a
addedn-sphere and closed unit ball compactness3576cc461c5f
addedAlaoglu's theorem6741194942dd
addedCantor set is compactd6a24a5d4fb5
addedPointwise convergence topology on functions67bcb011e379
addedArzelà–Ascoli theorem167b1f996c6a
addedLipschitz functions compact under uniform distancea13f6ed790c5
addedSpectrum of bounded linear operator is compact25c55b611929
addedSpace of Borel probability measures compactda204a8023bb
addedProkhorov's theorem8397966eeb4f
addedTight collection of probability measuresaebb43686e32
addedCompact real form of semisimple Lie group473fcbc520d9
addedp-adic integers homeomorphic to Cantor set68fb707ba12d
addedGlobal field quotient by adele ring compactb6cbd9c48506
addedSpectrum of commutative ring compact69050080d65d
addedSpectrum of Boolean algebra is compact22300f76a5ea
addedStructure space of Banach algebra compact80f114d79f93
addedHilbert cube is compact2854edcaf74f
addedProfinite group is compactdb7afa8268b5