Let K be a compact topological group, and let F be a set of continuous functions defined on K that has cardinality greater that continuum. Prove that there exist x0∈K and f \not\equal{}g \in F such that
f(x_0)\equal{}g(x_0)\equal{}\max_{x\in K}f(x)\equal{}\max_{x \in K}g(x).
I. Juhasz functionreal analysisreal analysis unsolved