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- Sorgenfrey_plane abstract "In topology, the Sorgenfrey plane is a frequently-cited counterexample to many otherwise plausible-sounding conjectures. It consists of the product of two copies of the Sorgenfrey line, which is the real line under the half-open interval topology. The Sorgenfrey line and plane are named for the American mathematician Robert Sorgenfrey.A basis for the Sorgenfrey plane, denoted from now on, is therefore the set of rectangles that include the west edge, southwest corner, and south edge, and omit the southeast corner, east edge, northeast corner, north edge, and northwest corner. Open sets in are unions of such rectangles.is an example of a space that is a product of Lindelöf spaces that is not itself a Lindelöf space. The so-called anti-diagonal is an uncountable discrete subset of this space, and this is a non-separable subset of the separable space . It shows that separability does not inherit to closed subspaces. Note that and are closed sets that cannot be separated by open sets, showing that is not normal. Thus it serves as a counterexample to the notion that the product of normal spaces is normal; in fact, it shows that even the finite product of perfectly normal spaces need not be normal.".
- Sorgenfrey_plane thumbnail Sorgenfrey_plane.png?width=300.
- Sorgenfrey_plane wikiPageID "682853".
- Sorgenfrey_plane wikiPageRevisionID "578490350".
- Sorgenfrey_plane hasPhotoCollection Sorgenfrey_plane.
- Sorgenfrey_plane subject Category:Articles_with_inconsistent_citation_formats.
- Sorgenfrey_plane subject Category:Topological_spaces.
- Sorgenfrey_plane type Abstraction100002137.
- Sorgenfrey_plane type Attribute100024264.
- Sorgenfrey_plane type MathematicalSpace108001685.
- Sorgenfrey_plane type Set107999699.
- Sorgenfrey_plane type Space100028651.
- Sorgenfrey_plane type TopologicalSpaces.
- Sorgenfrey_plane comment "In topology, the Sorgenfrey plane is a frequently-cited counterexample to many otherwise plausible-sounding conjectures. It consists of the product of two copies of the Sorgenfrey line, which is the real line under the half-open interval topology.".
- Sorgenfrey_plane label "Piano di Sorgenfrey".
- Sorgenfrey_plane label "Plan de Sorgenfrey".
- Sorgenfrey_plane label "Plano de Sorgenfrey".
- Sorgenfrey_plane label "Plano de Sorgenfrey".
- Sorgenfrey_plane label "Sorgenfrey plane".
- Sorgenfrey_plane label "Sorgenfrey-Ebene".
- Sorgenfrey_plane sameAs Sorgenfrey-Ebene.
- Sorgenfrey_plane sameAs Plano_de_Sorgenfrey.
- Sorgenfrey_plane sameAs Plan_de_Sorgenfrey.
- Sorgenfrey_plane sameAs Piano_di_Sorgenfrey.
- Sorgenfrey_plane sameAs Plano_de_Sorgenfrey.
- Sorgenfrey_plane sameAs m.032ml0.
- Sorgenfrey_plane sameAs Q1570438.
- Sorgenfrey_plane sameAs Q1570438.
- Sorgenfrey_plane sameAs Sorgenfrey_plane.
- Sorgenfrey_plane wasDerivedFrom Sorgenfrey_plane?oldid=578490350.
- Sorgenfrey_plane depiction Sorgenfrey_plane.png.
- Sorgenfrey_plane isPrimaryTopicOf Sorgenfrey_plane.
