On the finite-dimensionality of topological products

✍ Scribed by Boris A. Pasynkov

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 674 KB
• Volume: 82
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00064-9

✦ Synopsis

It is proved that there exist integers e(k, 1) 3 -1 for k, 1 = -1 , 0, 1, such that Ind X x Y < e(Ind X, Ind Y) if the space X x Y is normal (and Hausdorff), Y is locally compact paracompact (in particular, compact) and Ind X < co, Ind Y < co (therefore any normal product of two finitedimensional in the sense of Ind spaces, one of which is locally compact paracompact is finite-dimensional in the same sense). Analogous assertions hold for any strongly paracompact product, any normal product with one metrizable factor and any normal product of a pseudocompact space and a k-space. Also it is proved that a strongly paracompact or a z-embedded subspace of a finitedimensional in the sense of Ind normal space is finite-dimensional in the same sense.