Convergence concepts in semi-ordered linear spaces, I

Hidegorô Nakano, Masahumi Sasaki
1959 Proceedings of the Japan Academy  
Concerning semi-ordered linear spaces, L. Kantorovitch 1 gave originally two different concepts of convergence, that is, order convergence and star convergence. One of the authors introduced two other concepts, that is, dilatator convergence in 2 and individual convergence in 3, which are essentially equivalent to each other. Combining these concepts, we also obtain star-individual convergence in 4. In this paper we want to discuss these concepts of convergence and their combinations more
more » ... atically. In the sequel we will use the terminologies and notations in the book 4. Let R be a continuous semi-ordered linear space. We consider the order convergence basic, that is, for a sequence aeR (,----0, 1, 2, ..
doi:10.3792/pja/1195524457 fatcat:qhovge6rsbf2tabtvhdlgr6l2m