Functional equivalence of topological spaces

✍ Scribed by M.M. Choban

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 235 KB
• Volume: 111
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00186-8

✦ Synopsis

Let E be a non-trivial Banach space. The question when the spaces C p (X, E) and C p (Y, E) of all continuous mappings of X and Y into E in the topology of pointwise convergence are linearly homeomorphic is studied. These spaces are called l E -equivalent. A topological property or a cardinal function is called l E -invariant if it is preserved by the relation of the l E -equivalence. We prove that σ -discreteness, σ -scatteredness, the hereditary Lindelöf number, the hereditary density, the density, and the spread are l E -invariant properties. Moreover, we prove that in the class of µ-spaces of pointwise countable type the scatteredness, k-scatteredness, the extent, the paracompactness, and the p-paracompactness are l E -invariants. For that we introduce the notions of pm-equivalence, omequivalence, pom-equivalence. We study some functional functors.