Abstract
If S, T are semigroups with S⊂T, then the dominion of S in T, Dom(S,T), is the set of all x ε T such that for each semigroup U and for each pair of homomorphisms f,g: T→U with f|S=g|S, then f(x)=g(x). S is absolutely closed if Dom(S,T)=S for all T. That full transformation semigroups are absolutely closed has previously been reported. The intent here is to offer a corrected proof of that theorem.
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References
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Scheiblich, H.E., Moore, K.C. T X is absolutely closed. Semigroup Forum 6, 216–226 (1973). https://doi.org/10.1007/BF02389124
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DOI: https://doi.org/10.1007/BF02389124