Motivated by Vopěnka's conception of infinity as unsurveyability, I propose a property of fuzzy indistinguishability relations that represents limited discernment abilities of real-world agents. This property corresponds to the precompactness (i.e., total boundedness) of the pseudometrics dual to the fuzzy indistinguishability relation. I will show several properties of precompact approximation spaces that resemble finiteness or compactness and discuss their corollaries.