The lower and upper p-topological (p-regular) modifications for lattice-valued convergence spaces

In this paper, the notions of lower and upper topological (regular) modifications with respect to a stratified L-generalized convergence structure and those with respect to a stratified L-strong generalized convergence structure, are defined and studied. The basic properties and characterizations are presented. In particular, it is proved that the lower modifications behave reasonably well relative to final structures, whereas the upper modifications exhibit comparable behavior relative to initial structures.

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