On continua having three types of open subsets
For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum such that (a) ; (b) ; (c) ; (d) if β < ω(⁺), then is separable and first countable; (e) if n = 1, then can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then can be made chainable and hereditarily indecomposable. In particular,...