# Locally compact field

In algebra, a **locally compact field** is a topological field whose topology forms a locally compact space[1] (in particular, it is a Hausdorff space). Examples are discrete fields and local fields such as the field of complex numbers and the *p*-adic fields. Since one can always give discrete topology to a field, any field can be turned into a locally compact field.

## References

- Narici, Lawrence (1971),
*Functional Analysis and Valuation Theory*, CRC Press, pp. 21–22, ISBN 9780824714840.

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