# 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 == |

## 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.