Year: 2026
Type: article
Abstract: This research paper addresses several aspects of the structure of quasi- -normed spaces, which dates back to C. Park, as a broader class of quasi-modular spaces. It begins by reviewing the definition along with several diverse examples. Also, the derivation of a normed space, a quasi-normed space, and a quasi-2-metric space is presented from the current space and vice versa. The description of the ball in this space was presented as a non-convex, symmetric, balanced, and absorbing set, and this was proven. Topologically, it has been proven that the quasi-2-normed spaces are Hausdorff topological vector spaces upon the usual topology (a topology generated by a family of balls). Another topology by a separating family of a-quasi-norms has been defined, and its coincidence with the usual topological structure has been demonstrated. Throughout this study, the sufficient and necessary assumption for the normality of quasi- -normed spaces, and the sufficient assumption for the metrizability property, have been proven
DOI: 10.30526/39.4.4424
Authors: Intisar Kareem Atia, Salwa Salman Abed
Institution: University of Baghdad
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7223037447