Abstract.It has been observed by several authors that cartesian closed topological categories ensure many nice properties for any associated topological algebras. It turns out that a topological algebra can be cartesian closed without its topological component X being so. However, the algebra component A has to be cartesian closed. It is proved, under the assumptions that X is a cartesian closed well-fibred topological construct and A is a cartesian closed category of algebras with unary operations satisfying a minor condition, is cartesian closed.

Received: May 11, 2005

AMS Subject Classification: 08A25, 08A60, 08A30, 08C05, 17A30, 18A40, 18B99, 18D15, 54A05

Key Words and Phrases: topological category, cartesian closed, universal algebra, topological algebra

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 3