The Katětov dimension of proximity spaces

✍ Scribed by H. L. Bentley; M. Hušek; R. G. Ori

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 727 KB
• Volume: 4
• Category: Article
• ISSN: 0927-2852
• DOI: 10.1007/bf00124113

✦ Synopsis

An analogue of Kat~tov's theorem on the equality between the dimension of a Tychonov space and the analytic dimension of its ring of bounded real-valued continuous maps is established for proximity spaces and proximally continuous maps by an internal method of proof. A new kind of filter, called proximally prime filter, arises naturally as a tool in this theory.