Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λn), n ∈ N be an unbounded sequence numbers. Costakis has proved following result. There exists entire function f with property: for every x, y R 0 , θ ∈(0,1) a there is subsequence natural (mn), such that, compact subset L ⊆ In present paper we show that constant cannot replaced by any non-constant G. This so ev...

where Q is a continuous function of x and x—>Q(x, •) is continuous with respect to the £»(/*) norm. If it is also the case that ^ | T is dense in Li(ju)> then ()(•, 0) is a limit (uniform convergence on compact subsets of A) of functions in B. These results also give integral representations like (1) and (2) for a complex function algebra, simply by considering the space B of real parts of the ...