Pseudocompact and Stone-Weierstrass product spaces

Spaces of Rational Maps and the Stone-weierstrass Theorem

It is shown that Segal’s theorem on the spaces of rational maps from CP to CPn can be extended to the spaces of continuous rational maps from CPm to CPn for any m 6 n. The tools are the Stone-Weierstraß theorem and Vassiliev’s machinery of simplicial resolutions.

Pseudocompact Spaces

A Stone-weierstrass Type Theorem for Semiuniform Convergence Spaces

A Stone-Weierstraß type theorem for semiuniform convergence spaces is proved. It implies the classical Stone-Weierstraß theorem as well as a Stone-Weierstraß type theorem for filter spaces due to Bentley, Hušek and Lowen-Colebunders [1].

The Stone-weierstrass Theorem

The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of...

Maximal pseudocompact spaces

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compa...