Abstract
In this paper we provide a Heine–Borel type characterization for 0-compactness in approach spaces (Lowen 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). We then go on to characterize Hausdorffness for approach frames which allows us to study some fundamental properties of compact Hausdorff approach frames.
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Banaschewski, B., Lowen, R. & Van Olmen, C. Compact Hausdorff Approach Frames. Order 29, 105–118 (2012). https://doi.org/10.1007/s11083-011-9200-x
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DOI: https://doi.org/10.1007/s11083-011-9200-x