ON THE CARDINALITY OF COMPACTIFICATIONS OF DYADIC SPACES

It is shown that the supercardinality of a completely regular space equivalent to a dyadic space is equal to provided , where is the -weight of . In particular, it follows that the supercardinality of any countable dense subspace of a dyadic compactum of weight is equal to . This solves a problem raised by A. V. Arhangel'skiĭ on whether there exists a countable completely regular space whose every compactification has a cardinality larger than the continuum.Bibliography: 12 titles.