M. Aaly Kologani - Hatef Higher Education Institute, P.O. Box
G. R. Rezaei - Department of Mathematics, University of
R. A. Borzooei - Department of Mathematics, Shahid Beheshti
Y. B. Jun - Department of Mathematics, Education, Gyeongsang

Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “⊙”, “→” and “∧” in a hoop are uniformly continuous.

Hoop, quasi-valuation map, S⊙(S→, F)-quasi-valuation map, (pseudo) metric space