Let \(X\) be a uniform space with its uniformity generated by a set of pseudo-metrics \(\Gamma \). Let the symbol \(\simeq \) denote the infinitesimal relation on the nonstandard extension \(^{\ast }X,\) where \(x\simeq y\) means that \(^{\ast }\rho \left( x,y\right) \) is infinitesimal to \(0\) for each \( \rho \in \Gamma .\) This equivalence relation is useful for defining the nonstandard hull of a uniform space: if \( \text{fin}^{\ast }X\) denotes the set of all finite points then the nonstandard hull is the quotient of \( \text{fin}^{\ast }X\) modulo \(\simeq .\) If \(X\) is a uniform space with invariant nonstandard hull then \(\text{fin}^{\ast }X\) is equal to \(\text{pns}^{\ast }X,\) the set of all prenearstandard points. The author introduces a second equivalence relation \( \approx ,\) by defining \(x\approx y\) iff \(^{\ast }\rho \left( x,^{\ast }p\right) \simeq ^{\ast }\rho \left( y,^{\ast }p\right) \) for all \(p\in X\) and \(\rho \in \Gamma .\) Then \(x\simeq y\) implies \(x\approx y\) for all \( x,y\in \) \(^{\ast }X,\) and the two equivalence relations coincide on \( \text{ pns}^{\ast }X.\) A uniform space \(X\) is called an S-space if the two equivalence relations coincide on \(\text{fin}^{\ast }X.\) The author raises the question whether \(X\) is an S-space if and only if \( \text{fin} ^{\ast }X=\text{pns}^{\ast }X.\) The author gives a proof for the case that \(\Gamma \) consists of a single pseudo-metric \(\rho .\)