A sequence {fn} defined on set S is said to be uniformly bounded on S if
1
there exists k < 0 such that |fn(x)| < k; for all x belongs to S and n belongs to \(\mathbb N\).
2
there exists k > 0 such that |fn(x)| > k; for all x belongs to S and n belongs to \(\mathbb N\).
3
there exists k > 0 such that |fn(x)| < k; for all x belongs to S and n belongs to \(\mathbb N\).
4
there exists k < 0 such that |fn(x)| > k; for all x belongs to S and n belongs to \(\mathbb N\).