ABSTRACT
This chapter contains author’s research revolving around P. Roy space Δ and obtained between 1972–1978. The Roy method is applied to obtain N-compact spaces of positive dimension: the space μ and its metrizable subspaces μ0 and μ00. The chapter provides a description of a variant of Roy’s Δ, its main purpose is to make the relation between Δ and μ more transparent. It contains the proof that, under the continuum hypothesis, dimμ02=1; more detailed comments on this topic as well as on the contributions of J. Teresawa are provided. The properties of μ depend upon the selection of the sets A0, A and B; this topic was studied in the dissertation of D. Jakel; in particular, the proof of non–metrizability of the full μ can be found there.
