On the topology induced by fuzzy partial metric spaces

In recent years, fuzzy metric spaces and fuzzy partial metric spaces have attracted considerable attention due to their ability to generalize classical metric structures and model uncertainty in a more flexible and nuanced manner. In particular, fuzzy partial metrics extend fuzzy metrics by allowing different self-distances for points. Considering that each point's self-distance may vary in fuzzy partial metric spaces, the concept of an open ball is defined accordingly, differing from its definition in classical fuzzy metric spaces. One of the central problems in this area is the construction and comparison of topologies induced by different notions of open balls. In the existing literature, there are two commonly used notions of open balls, and it has been shown that a topology can be induced using only one of these concepts. In this study, we introduce a new notion of open balls in fuzzy partial metric spaces and demonstrate that a topology can be constructed from a fuzzy partial metric via the proposed concept. We further compare this notion with other variants of open balls and examine the corresponding induced topologies. Additionally, we investigate fundamental properties of this topology, including completeness, metrizability, and compactness, providing insight into how classical topological properties extend to the fuzzy partial metric setting.