Cakan, SumeyyeYilmazl, Yilmaz2024-08-042024-08-0420180369-82032250-1762https://doi.org/10.1007/s40010-017-0418-xhttps://hdl.handle.net/11616/98362Aseev (Proc Steklov Inst Math 2:23-52, 1986) started a new field in functional analysis by introducing the concept of normed quasilinear spaces which is a generalization of classical normed linear spaces. Then, we introduced the normed proper quasilinear spaces in addition to the notions of regular and singular dimension of a quasilinear space, Cakan and Yilmaz (J Nonlinear Sci Appl 8:816-836, 2015). In this study, we classify the normed proper quasilinear spaces as solid-floored and non solid-floored. Thus, some properties of normed proper quasilinear spaces become more comprehensible. Also we present the counterpart of classical Riesz lemma in normed quasilinear spaces.eninfo:eu-repo/semantics/closedAccessQuasilinear spacesFloor of an elementNormed proper quasilinear spacesSolid-floored quasilinear spacesRiesz lemma for normed quasilinear spacesArticle88223123910.1007/s40010-017-0418-x2-s2.0-85049131748Q4WOS:000436463000009Q4