Two examples of zero-dimensional sets in product spaces

✍ Scribed by Roman Pol

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 404 KB
• Volume: 33
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(89)80003-3

✦ Synopsis

Assuming the continuum hypothesis we give an example of a completely regular space F without any dense finite-dimensional subspace whose square Fx F contains a dense zero-dimensional subspace; the construction is based on an example of a metrizable separable space H whose all uncountable subsets are infinite-dimensional, but whose square H x H contains an uncountable zero-dimensional subset.