If metric space is interpreted generally enough, then there is no difference between topology and metric spaces theory (with continuous mappings). Building on ideas of Kopperman, Flagg …

A metric space is a set with a notion of distance defined between points of that set. This notion of distance is a function known as the metric (which must satisfy a set of axioms pertaining to …

What is the *exact* definition of a bounded subset in a metric space? Ask Question Asked 11 years, 9 months ago Modified 3 years, 3 months ago

Aug 9, 2024 · I just learned about metric spaces and their basic properties and definitions, such as the definition of a continuous function that maps two metric spaces. However, when I say …

A metric space is totally bounded if and only if every sequence has a Cauchy subsequence. (Try and prove this!) As you might suspect, this is basically equivalent to what Jonas has said. The …

May 29, 2015 · Metric spaces (and, more generally, topological spaces) occur all over the place. I am a working number theorist, and I use the concepts of topology (in all kinds of contexts, …

Jun 3, 2016 · Every separable metric space has a countable base Ask Question Asked 9 years, 7 months ago Modified 3 years, 11 months ago

A metric space is a topological space, since the metric induces a topology ("you can define open balls"). But a topological space may not be endowed by a metric ("open sets do not …

May 12, 2014 · 8 I've encountered the term of a "proper" metric space (a metric space is called proper if every closed, bounded subspace is compact), which struck as quite an interesting …

There is a theory of "metric measure spaces" which are metric spaces with a Borel measures, ie., a measure compatible with the topology of the metric space. It has a big literature that is well …