Assertion: metric space | /r/HasProperty | equivalent
Facets:
Source sentences:
text: A metric space M is compact if every sequence in M has a subsequence that converges to a point in M. This is known as sequential compactness and, in metric spaces (but not in general topological spaces), is equivalent to the topological notions of countable compactness and compactness defined via open covers.
text: Every extended metric can be transformed to a finite metric such that the metric spaces are equivalent as far as notions of topology (such as continuity or convergence) are concerned.
text: Later Addition: As it turns out, metric spaces and topological spaces are equivalent, if metric is interpreted broadly enough.