Difference between revisions of "Sorgenfrey Plane"

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== 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:
 
$$\mathbb{R}_\ell \times \mathbb{R}_\ell = \mathbb{R}^2_\ell$$
 
$$\mathbb{R}_\ell \times \mathbb{R}_\ell = \mathbb{R}^2_\ell$$
  

Revision as of 05:40, 1 December 2018

The Sorgenfrey Plane is an example of a product space of two Lindelöf spaces that is not itself Lindelöf.[1]

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.