Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  generalize Preuss' E -connectedness to lattice-valued convergence spaces and prove the basic theory for connected sets, including the product theorem.  further give a suitable definition of local E -connectedness and study its properties.
['Gunther Jäger']
I am writing a research paper on a idea Connectedness and local connectedness for lattice-valued convergence spaces
[{"from": "human", "value": "I am writing a research paper on a idea Connectedness and local connectedness for lattice-valued convergence spaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  generalize Preuss' E -connectedness to lattice-valued convergence spaces and prove the basic theory for connected sets, including the product theorem.  further give a suitable definition of local E -connectedness and study its properties."}]