Difference between revisions of "Sorgenfrey Plane"
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| − | The <strong>Sorgenfrey Plane</strong> is an example of a [[Product Topology|product]] [[Topological space|space]] of two [[Lindelöf]] spaces that is not itself Lindelöf.<ref>Munkres, James R. Topology, 2015. pg. 191.</ref> | + | The <strong>Sorgenfrey Plane</strong> is an example of a [[Product Topology|product]] [[Topological space|space]] of two [[Lindelöf]] spaces that is not itself Lindelöf.<ref>Munkres, James R. Topology, 2015. pg. 191.</ref> It should be noted that the Sorgenfrey plane is not [[Normal Space|normal]]. |
== Definition == | == Definition == | ||
| − | The Sorgenfrey Plane, named after mathematician [[Robert Sorgenfrey]], is defined as the [[Product Topology|product topology]] of two [[Lindelöf]] [[Topological space|space]]s | + | The Sorgenfrey Plane, named after mathematician [[Robert Sorgenfrey]], is defined as the [[Product Topology|product topology]] of two [[Lindelöf]] [[Topological space|space]]s: |
$$\mathbb{R}_\ell \times \mathbb{R}_\ell = \mathbb{R}^2_\ell$$ | $$\mathbb{R}_\ell \times \mathbb{R}_\ell = \mathbb{R}^2_\ell$$ | ||
Latest revision as of 05:42, 1 December 2018
The Sorgenfrey Plane is an example of a product space of two Lindelöf spaces that is not itself Lindelöf.[1] It should be noted that the Sorgenfrey plane is not normal.
Definition
The Sorgenfrey Plane, named after mathematician Robert Sorgenfrey, is defined as the product topology of two Lindelöf spaces: $$\mathbb{R}_\ell \times \mathbb{R}_\ell = \mathbb{R}^2_\ell$$
Further Reading
External Links
References
- ↑ Munkres, James R. Topology, 2015. pg. 191.
