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>
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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> 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, like so:
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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

  1. Munkres, James R. Topology, 2015. pg. 191.