Regular convergence 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...

Regular Convergence

$L-$ordered Fuzzifying Convergence Spaces

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

ON r-REGULAR CONVERGENCE

In his paper On sequences and limiting sets [ l ] , 1 G. T. Whyburn introduced the notion of regular convergence. He showed that in the cases of 0 and 1 regular convergence (see definition below) that the limit of sequences of many simple topological sets is of the same type as the members of the sequence. I t is the purpose of this paper to extend some of these results to higher dimensions. Th...

On statistical type convergence in uniform spaces

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.