Open AccessOn sublinear quasi-metrics and neighborhoods in locally convex cones
Author(s) -
Z. Yousefi,
M. R. Motallebi
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2203721y
Subject(s) - mathematics , sublinear function , subderivative , regular polygon , bounded function , convex analysis , metric (unit) , cone (formal languages) , convex set , pure mathematics , convex combination , mathematical analysis , convex optimization , geometry , algorithm , operations management , economics
We consider the topological structure of the sublinear quasi-metrics in locally convex cones and define the notion of a locally convex quasi-metric cone. The presence of upper bounded neighborhoods, gives necessary and sufficient conditions for the quasi-metrizability of locally convex cones. In particular, we investigate the boundedness and separatedness of locally convex quasi-metric cones and characterize the metrizability of locally convex cones.