T0 and T1 semiuniform convergence spaces

Completion of Semiuniform Convergence Spaces

Semiuniform convergence spaces form a common generalization of lter spaces (including symmetric convergence spaces and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform conver...

Stratified (L; M)-semiuniform convergence tower spaces

The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.

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].

Some Properties of (r, s)-T0 and (r, s)-T1 Spaces

CONVERGENCE APPROACH SPACES AND APPROACH SPACES AS LATTICE-VALUED CONVERGENCE SPACES

We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...