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- Locally_Hausdorff_space abstract "In mathematics, in the field of topology, a topological space is said to be locally Hausdorff if every point has an open neighbourhood that is a Hausdorff space under the subspace topology.Here are some facts: Every Hausdorff space is locally Hausdorff. Every locally Hausdorff space is T1. There are locally Hausdorff spaces where a sequence has more than one limit. This can never happen for a Hausdorff space. The bug-eyed line is locally Hausdorff (it is in fact locally metrizable) but not Hausdorff. The etale space for the sheaf of differentiable functions on a differential manifold is not Hausdorff, but it is locally Hausdorff. A T1 space need not be locally Hausdorff; an example of this is an infinite set given the cofinite topology. Let X be a set given the particular point topology. Then X is locally Hausdorff at precisely one point. From the last example, it will follow that a set (with more than one point) given the particular point topology is not a topological group. Note that if x is the 'particular point' of X, and y is distinct from x, then any set containing y that doesn't also contain x inherits the discrete topology and is therefore Hausdorff. However, no neighbourhood of y is actually Hausdorff so that the space cannot be locally Hausdorff at y. If G is a topological group that is locally Hausdorff at x for some point x of G, then G is Hausdorff. This follows from the fact that if y is a point of G, there exists a homeomorphism from G to itself carrying x to y, so G is locally Hausdorff at every point, and is therefore T1 (and T1 topological groups are Hausdorff).↑ ↑".
- Locally_Hausdorff_space wikiPageID "5075766".
- Locally_Hausdorff_space wikiPageLength "2778".
- Locally_Hausdorff_space wikiPageOutDegree "18".
- Locally_Hausdorff_space wikiPageRevisionID "638862678".
- Locally_Hausdorff_space wikiPageWikiLink Category:Properties_of_topological_spaces.
- Locally_Hausdorff_space wikiPageWikiLink Cofinite_topology.
- Locally_Hausdorff_space wikiPageWikiLink Cofiniteness.
- Locally_Hausdorff_space wikiPageWikiLink Differentiable_manifold.
- Locally_Hausdorff_space wikiPageWikiLink Differential_manifold.
- Locally_Hausdorff_space wikiPageWikiLink Etale_space.
- Locally_Hausdorff_space wikiPageWikiLink Hausdorff_space.
- Locally_Hausdorff_space wikiPageWikiLink Locally_metrizable.
- Locally_Hausdorff_space wikiPageWikiLink Mathematics.
- Locally_Hausdorff_space wikiPageWikiLink Metrization_theorem.
- Locally_Hausdorff_space wikiPageWikiLink Neighbourhood_(mathematics).
- Locally_Hausdorff_space wikiPageWikiLink Neighbourhood_(topology).
- Locally_Hausdorff_space wikiPageWikiLink Non-Hausdorff_manifold.
- Locally_Hausdorff_space wikiPageWikiLink Open_set.
- Locally_Hausdorff_space wikiPageWikiLink Particular_point_topology.
- Locally_Hausdorff_space wikiPageWikiLink Sheaf_(mathematics).
- Locally_Hausdorff_space wikiPageWikiLink Subspace_topology.
- Locally_Hausdorff_space wikiPageWikiLink T1_space.
- Locally_Hausdorff_space wikiPageWikiLink Topological_group.
- Locally_Hausdorff_space wikiPageWikiLink Topological_space.
- Locally_Hausdorff_space wikiPageWikiLink Topology.
- Locally_Hausdorff_space wikiPageWikiLinkText "Locally Hausdorff space".
- Locally_Hausdorff_space wikiPageWikiLinkText "Locally Hausdorff".
- Locally_Hausdorff_space wikiPageWikiLinkText "locally Hausdorff".
- Locally_Hausdorff_space hasPhotoCollection Locally_Hausdorff_space.
- Locally_Hausdorff_space wikiPageUsesTemplate Template:Refimprove.
- Locally_Hausdorff_space wikiPageUsesTemplate Template:Reflist.
- Locally_Hausdorff_space wikiPageUsesTemplate Template:Topology-stub.
- Locally_Hausdorff_space subject Category:Properties_of_topological_spaces.
- Locally_Hausdorff_space hypernym Space.
- Locally_Hausdorff_space type Property.
- Locally_Hausdorff_space type Space.
- Locally_Hausdorff_space comment "In mathematics, in the field of topology, a topological space is said to be locally Hausdorff if every point has an open neighbourhood that is a Hausdorff space under the subspace topology.Here are some facts: Every Hausdorff space is locally Hausdorff. Every locally Hausdorff space is T1. There are locally Hausdorff spaces where a sequence has more than one limit. This can never happen for a Hausdorff space.".
- Locally_Hausdorff_space label "Locally Hausdorff space".
- Locally_Hausdorff_space sameAs m.0d1m7c.
- Locally_Hausdorff_space sameAs Q6664659.
- Locally_Hausdorff_space sameAs Q6664659.
- Locally_Hausdorff_space wasDerivedFrom Locally_Hausdorff_space?oldid=638862678.
- Locally_Hausdorff_space isPrimaryTopicOf Locally_Hausdorff_space.