Abstract
For α∈N with α≥2, we define and characterize α-inflatable semigroups,S and establish that the product (βS/S,·)·(βS/S,·) of Stone-Ĉech remainders does not contain the closure of the minimal ideal of (βS,·), the Stone-Ĉech compactification ofS. From this result, one can easily derive Ruppert's result that the minimal ideal of a compact left-topological semigroup is not necessarily closed.
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Communicated by K. H. Hofmann
The author gratefully acknowledges support from Delaware State College under Grant No. 6769.
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Umoh, H. α-Inflatable semigroups. Semigroup Forum 44, 118–124 (1992). https://doi.org/10.1007/BF02574330
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DOI: https://doi.org/10.1007/BF02574330