Abstract
The purpose of this work is to present the concepts of a compact soft fuzzy metric space and totally fuzzy bounded space. The definition of a soft fuzzy metric space is first listed with its basic important properties. Then, the main theorems related to the compact soft fuzzy metric space and totally fuzzy bounded space concepts are proved. In particular, if is a soft fuzzy metric space with the property that is compact, then it is totally fuzzy bounded. Moreover, we prove the fact that a totally fuzzy bounded and a complete soft fuzzy metric space must be compact.
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