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On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

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 S n , α , β such that (a) d i m S n , α , β = n ; (b) t r D g S n , α , β = t r D g o S n , α , β = α ; (c) t r i n d S n , α , β = t r I n d S n , α , β = β ; (d) if β < ω(⁺), then S n , α , β is separable and first countable; (e) if n = 1, then S n , α , β can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then S n , α , β can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then S n , α , β can be made chainable and hereditarily indecomposable. In particular,...

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