# 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 | + | 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

- ↑ Munkres, James R. Topology, 2015. pg. 191.