Abstract
In the following text we compute possible heights of A (Alexandroff square), O (unit square [0, 1] × [0, 1] with lexicographic order topology) and U (unit square [0, 1] × [0, 1] with induced topology of Euclidean
plane). We prove Ph(A) = {n : n ≥ 5} ∪ {+∞}, Ph(O) = {n : n ≥
4} ∪ {+∞}, Ph(U) = {n : n ≥ 1} ∪ {+∞} (where for topological space
X, by Ph(X) we mean the collection of heights of transformation groups
with phase space X. Additionally we show that there is no topological
transitive (resp. Devaney chaotic) transformation group (G, A).
Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar, Reza Yaghmaeian, Hamed Yahyaoghli. (2020) Possible Heights of Alexandroff Square Transformation Groups, Punjab University Journal of Mathematics, Volume 52 , Issue 6.
-
Views
679 -
Downloads
57
Article Details
Volume
Issue
Type
Language
