Metrizability of ordered additive groups (Q763968)

The authors investigate metrizability of an ordered field with the order topology. Among the many results, one of the main ones is the following Theorem 2.2: For every ordered field \(K\), \(K\) is metrizable if and only if there exists an infinite subset \(A\) of the unit interval \([0,1]\) such that for each continuous function \(f:[0,1]\to K\), \(f[A]\) has a maximum.