On Dimensionsgrad, resolutions, and chainable continua

• Autorzy: Michael G. Charalambous , Jerzy Krzempek
• Języki publikacji: EN

Abstrakty

EN

For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(𝔠⁺), where ω(𝔠⁺) is the first ordinal of cardinality 𝔠⁺, we construct a continuum $S_{n,α,β}$ such that
(a) $dim S_{n,α,β} = n$;
(b) $trDg S_{n,α,β} = trDgo S_{n,α,β} = α$;
(c) $trind S_{n,α,β} = trInd₀S_{n,α,β} = β$;
(d) if β < ω(𝔠⁺), 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(𝔠⁺), then $S_{n,α,β}$ can be made hereditarily indecomposable;
(g) if n = 1 and α = β < ω(𝔠⁺), then $S_{n,α,β}$ can be made chainable and hereditarily indecomposable.
In particular, we answer the question raised by Chatyrko and Fedorchuk whether every non-degenerate chainable space has Dimensionsgrad equal to 1. Moreover, we establish results that enable us to compute the Dimensionsgrad of a number of spaces constructed by Charalambous, Chatyrko, and Fedorchuk.

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 3
• Strony: 243-265

Daty

wydano

2010

Twórcy

autor

Michael G. Charalambous

• Department of Mathematics, University of the Aegean, 83 200, Karlovassi, Samos, Greece

autor

Jerzy Krzempek

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Identyfikatory

DOI

10.4064/fm209-3-3