Strong general position and Menger curves
type: Item
instance of: scholarly article
title: Strong general position and Menger curves
zbMATH Open document ID: 0991.57026
DOI: 10.1016/S0166-8641(01)00006-2
author: Troy L. Goodsell
published in: Topology and its Applications
publication date: 2002-06-27T00:00:00Z
review text: The notion of strong general position for a finite simplicial complex in \(\mathbb R^n\) extends to a countable complex by ensuring that the coordinates of the vertices are algebraically independent. This then ensures that every hyperplane \(H\) meets at most \(\frac{(n-\text{dim}H)(1+\dim H)}{n-m-\dim H}\) simplices of dimension at most \(m<n-\dim H\). The ideas are then applied to Menger curves where the same bounds are achieved.
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N75
Mathematics Subject Classification ID: 57N37
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57N12
Mathematics Subject Classification ID: 57N15
zbMATH DE Number: 1760994
reviewed by: David B. Gauld
MaRDI profile type: Publication
cites work: On topological infinite deficiency
cites work: Q4069378
cites work: Characterizing 𝑘-dimensional universal Menger compacta
cites work: On compacta with convex projections
cites work: The visible set of a compactum in \(\mathbb{R}^n\)
description: scientific article; zbMATH DE number 1760994