ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

On fuzzy normed spaces

Valentin Gregori, Juan A. Mascarell, Salvador Romaguera Universidad Politécnica de Valencia, Spain

According to the notion of a fuzzy metric due to George and Veeramnai, we give a concept of fuzzy norm which permits us, in a similar way to the classic case, to induce a fuzzy metric which is invariant for (fuzzy)traslation. We also prove that each normed linear space can be endowed with the structure of a fuzzy normed space.

Although we do not know if the converse holds, we show that the topological space induced by a fuzzy normed space has the structure of a topological linear space.

Mathematics Subject Classification 54A40.

Key words and phrases: fuzzy metric, fuzzy norm.