For compact Hausdorff admissible right topological (CHART) group G, we prove w(G)=πχ(G). This equality is well known for groups. implies the criteria metrizability of CHART groups: if G first-countable (2013, Moors, Namioka) or Fréchet Glasner, Megrelishvili), has countable π-character (2022, Reznichenko) then metrizable. Under continuum hypothesis (CH) assumption, a sequentially Namioka's theo...