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