Analogs of Cantor manifolds for transfinite dimensions
type: Item
instance of: scholarly article
title: Analogs of Cantor manifolds for transfinite dimensions
zbMATH Open document ID: 0642.54028
DOI: 10.1007/BF01138729
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: The existence of bicompacta, homogeneous in the sense of transfinite small inductive dimension is considered. For every \(\alpha \leq \omega_ 1\) there exists a denumerably dimensional compact \(C^{\alpha}\) such that \(ind_ xC^{\alpha}\geq \alpha\) for every \(x\in C^{\alpha}\). For every \(\alpha <\omega_ 1\) there exists a separable first-countable bicompact \(Y_{\alpha}\) such that \(y_{\alpha}\) is an ind-manifold of the class \(\alpha\), ind \(Y_{\alpha}=\alpha +1\).
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54C99
zbMATH DE Number: 4046662
zbMATH Keywords: homogeneous bicompacta
zbMATH Keywords: transfinite small inductive dimension
zbMATH Keywords: separable first-countable bicompact
author: Vitalij A. Chatyrko
reviewed by: Dušan Adnadjević
MaRDI profile type: Publication
cites work: Q3257293
cites work: A lower bound for transfinite dimension
cites work: Spaces of transfinite dimensionality
cites work: Shuffling Ordinals and Transfinite Dimension
cites work: On snakelike bicompacta
description: scientific article; zbMATH DE number 4046662