Abstract
Supercomplete topological spaces and other variants of supercompleteness are defined in this paper. The main idea is to give different characterizations of Čech complete spaces. In particular it is shown that for paracompacta (and so for metrizable spaces) and topological groups the two notions of supercompleteness and Čech completeness coincide.
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Buhagiar, D., Pasynkov, B.A. Supercomplete topological spaces. Acta Math Hung 115, 269–279 (2007). https://doi.org/10.1007/s10474-007-5243-2
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DOI: https://doi.org/10.1007/s10474-007-5243-2