caa a22 4500 445345063 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00233-010-9262-x doi (NATIONALLICENCE)springer-10.1007/s00233-010-9262-x Ultrafilter semigroups generated by direct sums [Elektronische Daten] [Onesmus Shuungula, Yevhen Zelenyuk, Yuliya Zelenyuk] Let λ be an infinite cardinal and for every ordinal α<λ, let A α be a set with a distinguished element 0α∈A α. The direct sum of sets A α, α<λ, is the subset $X=\bigoplus_{\alpha<\lambda}A_{\alpha}$ of the Cartesian product ∏α<λ A α consisting of all x with finite supp (x)={α<λ:x(α)≠0α}. Endow X with a topology by taking as a neighborhood base at x∈X the subsets of the form {y∈X:y(α)=x(α) for all α<γ} where γ<λ. Let Ult (X) denote the set of all nonprincipal ultrafilters on X converging to 0∈X. There is a natural partial semigroup operation on X which induces a semigroup operation on Ult (X). We show that if direct sums X and Y are homeomorphic, then the semigroups Ult (X) and Ult (Y) are isomorphic. Springer Science+Business Media, LLC, 2010 Stone-Čech compactification nationallicence Ultrafilter semigroup nationallicence Direct sum nationallicence Local isomorphism nationallicence Shuungula Onesmus School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut Zelenyuk Yevhen School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut Zelenyuk Yuliya School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut Semigroup Forum Springer-Verlag 82/2(2011-04-01), 252-260 0037-1912 82:2<252 2011 82 233 https://doi.org/10.1007/s00233-010-9262-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9262-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shuungula Onesmus School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut NATIONALLICENCE 700 1- Zelenyuk Yevhen School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut NATIONALLICENCE 700 1- Zelenyuk Yuliya School of Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/2(2011-04-01), 252-260 0037-1912 82:2<252 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer