Open AccessTopological transitivity of the normalized maps induced by linear operators
Author(s) -
Pabitra Narayan Mandal
Publication year - 2022
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2022.15613
Subject(s) - mathematics , transitive relation , linear map , simple (philosophy) , dimension (graph theory) , pure mathematics , transformation (genetics) , infinity , space (punctuation) , linear space , projective test , linear operators , topology (electrical circuits) , discrete mathematics , combinatorics , mathematical analysis , computer science , bounded function , philosophy , biochemistry , chemistry , epistemology , gene , operating system
In this article, we provide a simple geometric proof of the following fact: The existence of transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well.