Boundedness of linear order-homomorphisms in $L$-topological vector spaces

Document Type: Research Paper

Authors

1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

2 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Abstract

A new definition of boundedness of linear order-homomorphisms (LOH)
in $L$-topological vector spaces is proposed. The new definition is
compared with the previous one given by Fang [The continuity of
fuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)
829$-$838]. In addition, the relationship between boundedness and
continuity of LOHs is discussed. Finally, a new uniform boundedness
principle in $L$-topological vector spaces is established in the
sense of a new definition of uniform boundedness for a family of
LOHs.

Keywords


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