Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   provide a Heine–Borel type characterization for 0-compactness in approach spaces (Lon 1997). Since this requires making use of the so-called regular function frame the most natural setting to develop this in is approach frames (Banaschewski 1999; Banaschewski et al., Acta Math Hung 115(3):183–196, 2007, Topology Appl 153:3059–3070, 2006).  then go on to characterize Hausdorffness for approach frames which allows us to study some fundamental properties of compact Hausdorff approach frames.
['Bernhard Banaschewski', 'R. Lowen', 'Christophe Van Olmen']
I am writing a research paper on a idea Compact Hausdorff approach frames
[{"from": "human", "value": "I am writing a research paper on a idea Compact Hausdorff approach frames"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   provide a Heine\u2013Borel type characterization for 0-compactness in approach spaces (Lon 1997). Since this requires making use of the so-called regular function frame the most natural setting to develop this in is approach frames (Banaschewski 1999; Banaschewski et al., Acta Math Hung 115(3):183\u2013196, 2007, Topology Appl 153:3059\u20133070, 2006).  then go on to characterize Hausdorffness for approach frames which allows us to study some fundamental properties of compact Hausdorff approach frames."}]