A one-point compactification for lattice-valued convergence spaces

We define a lattice-valued one-point compactification for a non-compact lattice-valued T2-space and find criteria when it is smaller than another T2-compactification of the same space. Also the concept of local boundedness is introduced and characterized using the lattice-valued one-point compactification and the lattice-valued Richardson compactification. ► We define a lattice-valued one-point compactification for a non-compact lattice-valued T2-space. ► We find criteria when it is smaller than any other T2-compactification of the same space. ► Local boundedness is defined and characterized by the lattice-valued one-point compactification and the lattice-valued Richardson compactification.