Spaces l-Dominated by I or R

2015/10/19 by Paul Gartside, Gartside, Paul, Ziqin Feng +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Advanced Banach Space Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1510.05589

Abstract

If X is compact metrizable and has finite fd-height then the unit interval, I, ℓ-dominates X, in other words, there is a continuous linear map of C_p(I) onto C_p(X). If the unit interval ℓ-dominates a space X then X is compact metrizable and has countable fd-height. Similar results are given for spaces ℓ-dominated by the reals.

Cited by

• Topological groups from matrices of sets

Related

• Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts
• On the class of NY compact spaces of finitely supported elements and related classes
• Properties D and aD are different
• Box and Nabla Products that are D-Spaces
• Locally n-connected compacta and UVⁿ-maps