Abstract
The main purpose of this paper is to introduce two new fuzzifying bornologies induced by fuzzy pseudo-norms. It is proved that these new fuzzifying bornologies are compatible with the vector structure. With the help of concrete examples, it is presented that these special kinds of fuzzifying bornologies are different from an example (introduced by Šostak and Uļjane, 2016 [23]) of a fuzzifying bornology. It is shown that the degree to which a sequence is convergent to a point bornologically is equal to the degree to which this sequence is convergent to above point topologically in fuzzy pseudo-normed linear spaces. Moreover, it is presented that V. Neumann fuzzifying bornology is separated in fuzzy pseudo-normed linear spaces if and only if the fuzzifying topology determined by a fuzzy pseudo-norm is Hausdorff.
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