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We show how group mapping semigroups can be considered as regular covers of their right letter mapping image and relate this to their graph of fibers. <\/jats:p>","DOI":"10.1142\/s0218196721400051","type":"journal-article","created":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T02:14:46Z","timestamp":1622859286000},"page":"1065-1091","source":"Crossref","is-referenced-by-count":2,"title":["Degree 2 transformation semigroups as continuous maps on graphs: Foundations and structure"],"prefix":"10.1142","volume":"31","author":[{"given":"Stuart","family":"Margolis","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel"}]},{"given":"John","family":"Rhodes","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, California 94720, USA"}]}],"member":"219","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"S0218196721400051BIB001","first-page":"239","volume-title":"Proc. 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