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Ayatollah Zadeh Shirazi, Fatemah, Mahmoodi, Mohammad Ali, Raeisi, Morvarid. (1394). On distality of a transformation semigroup with one point compactification of a discrete space as phase space. , (), -. doi: 10.22099/ijsts.2015.3180
Fatemah Ayatollah Zadeh Shirazi; Mohammad Ali Mahmoodi; Morvarid Raeisi. "On distality of a transformation semigroup with one point compactification of a discrete space as phase space". , , , 1394, -. doi: 10.22099/ijsts.2015.3180
Ayatollah Zadeh Shirazi, Fatemah, Mahmoodi, Mohammad Ali, Raeisi, Morvarid. (1394). 'On distality of a transformation semigroup with one point compactification of a discrete space as phase space', , (), pp. -. doi: 10.22099/ijsts.2015.3180
Ayatollah Zadeh Shirazi, Fatemah, Mahmoodi, Mohammad Ali, Raeisi, Morvarid. On distality of a transformation semigroup with one point compactification of a discrete space as phase space. , 1394; (): -. doi: 10.22099/ijsts.2015.3180

On distality of a transformation semigroup with one point compactification of a discrete space as phase space

Iranian Journal of Science
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 شهریور 1394
نوع مقاله: Regular Paper
شناسه دیجیتال (DOI): 10.22099/ijsts.2015.3180
نویسندگان
Fatemah Ayatollah Zadeh Shirazi* 1؛ Mohammad Ali Mahmoodi2؛ Morvarid Raeisi2
1Faculty of Mathematics, Statistics and Compyter Sience, College of Science, University of Tehran, Tehran, Iran
2Faculty of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
چکیده
For infinite discrete topological space Y, suppose A(Y) is one point compactification of , in the following text we prove that the transformation semigroup (A(Y) , S) is distal if and only if the enveloping semigroup E(A(Y) , S), is a group of homeomorphisms on A(Y), or equivalently for all p  E(A(Y) , S), p: A(Y)  A(Y) is pointwise periodic.
Also the transformation group (A(Y) , S) is distal (resp. equicontinuous, pointwise minimal) if and only if for all x  A(Y), xS is a finite subset of A(Y).
The text is motivated with Tables, Counterexamples and studying finally distality (and co-decomposability to distal transformation semigroups) in abelian transformation semigroup (A(Y) , S).
کلیدواژه‌ها
Alexandroff compactification؛ Distal؛ Finally distal؛ Fort space؛ One point compactification
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