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---
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).
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