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

Abstract

In this paper, a connectedness in stratified L-generalized convergence spaces, is defined and discussed. This connectedness is different from Jäger’s connectedness, 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

Key words:

• Lattice-valued convergence space
• connectedness
• separated sets

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 11501278, 11471152).