G. Rano - Department of Mathematics, Visva-Bharati, Santiniketan-۷۳۱۲۳۵, West Ben- gal, India
T. Bag - Department of Mathematics, Visva-Bharati, Santiniketan-۷۳۱۲۳۵, West Ben- gal, India
S. K. Samanta - Department of Mathematics, Visva-Bharati, Santiniketan-۷۳۱۲۳۵, West Bengal, India

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

Quasi-norm, ~Generating space, ~Fuzzy norm, ~ t-norm