Abstract
Uniform spaces are the carriers of notions such as uniform convergence, uniform continuity, precompactness, etc.. In the case of metric spaces, these notions were easily defined. However, for general topological spaces such distance- or size-related concepts cannot be defined unless we have somewhat more structure than the topology itself provides. So uniform spaces lie between pseudometric spaces and topological spaces, in the sense that a pseudometric induces a uniformity and a uniformity induces a topology.
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Kotzé, W. (1999). Uniform Spaces. In: Höhle, U., Rodabaugh, S.E. (eds) Mathematics of Fuzzy Sets. The Handbooks of Fuzzy Sets Series, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5079-2_10
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DOI: https://doi.org/10.1007/978-1-4615-5079-2_10
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