LEADER 02304nam 2200445 450 001 996418257903316 005 20210226090905.0 010 $a3-030-55215-2 024 7 $a10.1007/978-3-030-55215-2 035 $a(CKB)4100000011435812 035 $a(DE-He213)978-3-030-55215-2 035 $a(MiAaPQ)EBC6348314 035 $a(PPN)250220490 035 $a(EXLCZ)994100000011435812 100 $a20210226d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProfinite semigroups and symbolic dynamics /$fJorge Almeida [and three others] 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (IX, 278 p. 67 illus., 4 illus. in color.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v2274 311 $a3-030-55214-4 330 $aThis book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2274. 606 $aProfinite groups 615 0$aProfinite groups. 676 $a512.2 700 $aAlmeida$b Jorge$01005289 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418257903316 996 $aProfinite semigroups and symbolic dynamics$92311010 997 $aUNISA