Basic intervals in the partial order of metrizable topologies (Q1295343)

Intervals in the poset of all metrizable topologies on a set \(X\) are studied. It is shown that there are no nontrivial finite intervals and that, assuming the Continuum Hypothesis, there are exactly two isomorphisms classes of basic intervals. (An interval \([\sigma,\tau]\) is basic if \(\sigma\) and \(\tau\) differ at at most one point).