# Category:Tychonoff's Theorem

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This category contains pages concerning **Tychonoff's Theorem**:

### General Theorem

Let $I$ be an indexing set.

Let $\family {X_i}_{i \mathop \in I}$ be an indexed family of non-empty topological spaces.

Let $\ds X = \prod_{i \mathop \in I} X_i$ be the corresponding product space.

Then $X$ is compact if and only if each $X_i$ is compact.

## Pages in category "Tychonoff's Theorem"

The following 8 pages are in this category, out of 8 total.

### T

- Tychonoff's Theorem
- Tychonoff's Theorem for Hausdorff Spaces
- Tychonoff's Theorem/General Case
- Tychonoff's Theorem/General Case/Proof 1
- Tychonoff's Theorem/General Case/Proof 2
- Tychonoff's Theorem/General Case/Proof 2/Lemma 1
- Tychonoff's Theorem/General Case/Proof 2/Lemma 2
- Tychonoff's Theorem/General Case/Proof 2/Lemma 3