Dimension Theory via Reduced Bisector Chains

Janos, Ludvik

Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 305-311

Résumé

Let (X, d) be a metric space and Y and Z subsets of X. We say that Z is a bisector in Y and write Y⊳Z iff Y⊃Z and there are two distinct points y1, y2 ∈ Y such that Z = ={z:d(z, y1) = d(z, y2) and z∈Y}. By a reduced bisector chain in (X, d) of length n we understand a chain X = such that dim Xn≤0 and dimXn-1>0). By r(X, d) we denote the maximum length of reduced bisector chains in (X, d). For a metrizable topological space X we introduce the topological invariant r(X) as the minimum of r(X, d) taken over the set of all metrizations d of X. We prove that the function r(X) coincides with the dimension of X on the class of compact metric spaces.

Détail

DOI : 10.4153/CMB-1978-053-9

Mots-clés : 54 F 45, 55 C 10, 54 E 35, Bisector, bisector-chain, dimension, metrization, topological invariant, expressability of a topological property in a suitable language