---
title: Tychonoff Product Theorem
parent: Compactness
grand_parent: General Topology
nav_order: 2
---

# {{ page.title }}

{% theorem * Tychonoff Product Theorem %}
The product of (an arbitrary family of) compact spaces is compact.
{% endtheorem %}

{% proof %}
TODO
{% endproof %}

Important Application:
[Banach–Alaoglu Theorem](/pages/functional-analysis-basics/banach-alaoglu-theorem.html).