Connectedness for lattice-valued subsets in lattice-valued convergence spaces

Abstract

In this paper, a connectedness in stratied L-generalized convergence spaces, is defined and discussed. This connectedness is different from Jäger's con- nectedness, in particular, it is defined for L-subsets however Jäger's connectedness is defined for crisp subsets. Thus this give a partly answer to Jäger's question in 2016: define a connectedness for L-subsets in lattice-valued convergence spaces. Then the basic properties of this connectedness are discussed.

Mathematics Subject Classification (2010): 54A40, 06D10.

Keywords: Lattice-valued convergence space, connectedness, separated sets