On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, and Jerzy Krzempek. "On Dimensionsgrad, resolutions, and chainable continua." Fundamenta Mathematicae 209.3 (2010): 243-265. <http://eudml.org/doc/282600>.

@article{MichaelG2010,
abstract = {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) $dim S_\{n,α,β\} = n$; (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(⁺), 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, 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.},
author = {Michael G. Charalambous, Jerzy Krzempek},
journal = {Fundamenta Mathematicae},
keywords = {Dimensionsgrad; inductive dimension; non-coinciding dimensions; chainable continuum; resolution; atomic map; fully closed map},
language = {eng},
number = {3},
pages = {243-265},
title = {On Dimensionsgrad, resolutions, and chainable continua},
url = {http://eudml.org/doc/282600},
volume = {209},
year = {2010},
}

TY - JOUR
AU - Michael G. Charalambous
AU - Jerzy Krzempek
TI - On Dimensionsgrad, resolutions, and chainable continua
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 3
SP - 243
EP - 265
AB - 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) $dim S_{n,α,β} = n$; (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(⁺), 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, 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.
LA - eng
KW - Dimensionsgrad; inductive dimension; non-coinciding dimensions; chainable continuum; resolution; atomic map; fully closed map
UR - http://eudml.org/doc/282600
ER -