Remark 1

To make the language more expressive we may use the expressions "$x$ is close enough to $y$" and "$x$ and $y$ are as close as we please" in some statements. For example, we shall say that a relation

R $\{ x, y \}$ is true whenever $x$ and $y$ are close enough if there is an entourage $V$ such that the relation $(x, y) \in V$ implies $R \{ x, y \}$.