Degrees of Separation Properties in Stratified L-Generalized Convergence Spaces Using Residual Implication

Abstract

By using the residual implication on a frame L, we develop a theory of separation axioms in the category of lattice-valued convergence spaces in the spirit of Lowen, i.e., we define for each space some degrees of fulfilling T_0, T_1, T_2 and regularity axioms from a logical aspect. These degrees of separation axioms generalize the theory of separation axioms in the sense of Jager.