## Getting acquainted with compact sets

### Task number: 3171

Determine whether the following subsets in \(\mathbb R^n\) are compact (justify your answer):

#### Variant 1

\([0, 1]\times[0, 1]\times[0, 1]\)

#### Variant 2

\(\{(x, y, z) \in \mathbb R^3: |x + y + z| \leq 1\}\)

#### Variant 3

\(\{(x, y, z) \in \mathbb R^3: |x + y| + z \leq 1\}\)

#### Variant 4

\(\{(x, y) \in \mathbb R^2: x^4 + y^4 < 10\}\)

#### Variant 5

\(\{\frac1n: n \in \mathbb N\} \cup \{0\}\)