Unal, CihanAydin, Ismail2025-03-232025-03-2320230009-725X1973-4409https://doi.org/10.1007/s12215-022-00776-1https://hdl.handle.net/11486/6791In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We discuss fine topology and compare this topology with Euclidean one. Finally, we give some information about importance of the fine topology in the potential theory.eninfo:eu-repo/semantics/closedAccessFine topologyThinnessRelative capacityWeighted variable exponent Sobolev spacesArticle7231863187710.1007/s12215-022-00776-12-s2.0-85132829668Q1WOS:000815748500002N/A