Revision #150 → #1257 · back to history
addedGeneral topologyeddecda30317
addedTopology on a set145b5ae2bcf1
addedTopological space89edab6139cf
addedOpen and closed sets0c3e29b9eab0
addedBase (basis) for a topology40c1d5ac6670
addedSubspace topology1ca028e4ee58
addedProduct topologybb5a6196afa9
addedQuotient topologyc7841bc2dfb4
addedDiscrete topology985a58ab45f4
addedTrivial (indiscrete) topology07dba93fae75
addedCofinite topology06c768745fe5
addedCocountable topology2554c5ecdadb
addedStandard topology on R3f28d96cc6eb
addedLower limit topologyfae89cd793bb
addedMetric topology1c683bb7bd38
addedFinite topological spacesf8f0c485de2c
addedNatural topology on a manifoldaa122eace5e1
addedZariski topology1e506ceeebc8
addedSierpiński space839e53e42dac
addedOrder topology on an ordinal0053450a4b05
addedContinuity (neighborhood)42b6b5449a49
addedFunctions out of a discrete space are continuousad301e819f83
addedFunctions out of an indiscrete space070c781e9238
addedNeighborhood definition of continuityaa8a0993e1c5
addedContinuity via limit (Hausdorff target)f60d6291b7c3
addedContinuity at isolated points233dcc74da51
addedContinuity and limitsb478718e0382
addedSequentially continuous function8b79b9256853
addedContinuous implies sequentially continuous70be78333b23
addedConverse for first-countable spaces760cbff69615
addedContinuity characterized by nets00b57af74f44
addedClosure and interior operatorsf4203227b37b
addedContinuity via closure operator0ffabacd3686
addedComposition of continuous functionsca416981adb4
addedContinuous image of compact space57135a970538
addedContinuous image of connected spaceee52fd0f8624
addedContinuous image of path-connected space81b4a53bfb56
addedContinuous image of Lindelöf spacedbac9016d78f
addedContinuous image of separable spacec910023ecae1
addedCoarser and finer topologies84b7f2187926
addedIdentity map and comparison of topologiesa063e7b0fce5
addedOpen mapf5717bfb4180
addedHomeomorphismbb9829a0ff50
addedContinuous bijection compact to Hausdorff is homeomorphisma2e938cf4a65
addedFinal topology9f0ab36d9dfb
addedInitial topology778e2c0962d0
addedTopology determined by continuous functions8343351f9778
addedCompact spacee4112877cf99
addedQuasi-compact (Bourbaki terminology)22bf6408d7e1
addedClosed intervals in R are compactebe886d8eb69
addedHeine–Borel theorem5096e5bb9cc4
addedContinuous image of compact is compactae7ae9f02bd9
addedCompact subset of Hausdorff is closed500305f2ba6f
addedContinuous bijection compact to Hausdorff1177947c9ef8
addedSequential compactness of compact metric spaces8f71cbda6286
addedEmbedding of compact manifoldsb2e41e8bc6c4
addedConnected and disconnected spaces4c2313553fad
addedEquivalent conditions for connectedness28e846baf1ff
addedIntervals in R are connected15aa1eee8f52
addedContinuous image of connected spaceaf6e7284546a
addedConnected components2087c8848404
addedComponents form a partitionba38bcb67284
addedQuasi-component equals component under conditions344d7b41ac6c
addedTotally disconnected space348cb483d33f
addedTotally separated space17636b19319d
addedTotally separated implies totally disconnected5afc2b180bd2
addedPath-component8f11d4ae48f1
addedPath-connected space3c6459f1ea96
addedPath-connected implies connected57c5b75a2025
addedConnected but not path-connected spaces06a2db865acb
addedConnected iff path-connected for subsets of R119faf4e205c
addedConnectedness equals path-connectedness for finite spaces0d37dbc45821
addedProduct topologyb4951f6f29c5
addedBasis for finite productsb692df66f53b
addedSubbase for product topologycd26cdc830d7
addedBox topology35034f60b708
addedBox topology finer than product topology8a7b4a7da03c
addedTychonoff's theorem877f070d2ae0
addedT0 (Kolmogorov) space3b2efa1cc5ee
addedT1 (Fréchet) spacea771405a11c7
addedHausdorff (T2) space05c759bc80bc
addedUrysohn (T2½) spacefe231a409141
addedRegular (T3) spacec83a73ea30c1
addedTychonoff (T3½) space8abfeefe53e7
addedNormal (T4) space98236e96dc71
addedUrysohn's lemma37db9d5ded63
addedCompletely normal (T5) spaced6ad83e35f1c
addedPerfectly normal (T6) spaceefa08f02f8fc
addedTietze extension theorema9e704077426
addedAxiom of countabilityb9bd7ed24fcd
addedSequential space8b5cbc6bcf0d
addedFirst-countable space0ef8626bf7f9
addedSecond-countable space0f6201f4d378
addedSeparable space3a6a7327f000
addedLindelöf spacee74561385a91
addedσ-compact space30b849c7903b
addedFirst-countable implies sequential6eea23a7246c
addedSecond-countable implicationsb2f28179f939
addedσ-compact implies Lindelöf5fdff6d821e5
addedMetric space is first-countablee01584176022
addedEquivalences for metric spaces7e3e408c7cf7
addedMetric space87c31e837dd1
addedMetric spaces are paracompact, Hausdorff, normalca46b63d1f81
addedMetrization theorems37f368c0b77e
addedBaire category theoremb12b8ec6cd8a
addedOpen subspace of a Baire space003c73eb2c6b
addedContinuum3516423c6f16
addedTopological algebra807d115a4715
addedUnital associative topological algebra is a topological ringe081b666f1a1
addedMetrizable space7e1d9d91632b