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

In this paper, a connectedness in stratied L -generalized convergence spaces, is defined and discussed. This connectedness is different from J a ger's con- nectedness, in particular, it is defined for L -subsets however J a ger's connectedness is defined for crisp subsets. Thus this give a partly answer to J a ger'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