Is every metric space compact?
95993
Isn't every subset of a compact space compact?
99816
Existence of Topologically Transitive Maps on nice Metric Spaces
121135
Why don't we use closed covers to define compactness of metric space?
29744
Compactness and axiomatisability
157753
Show that any set in a metric space can be written as the intersection of open sets
133504
Suppose $X$ is a metric space and $S \subseteq X.$ Then, $S^o=\{x \in X~|~dist(x,S^c)>0\}$.
49374
Closure of a subset in a metric space
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
16060
Showing this metric space is complete
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
72950
Book recommendation for Metric Spaces
152493
Is an expanding map on a compact metric space continuous?
74877
Every metric space with a countable base is separable
7402
Showing a compact metric space has a countable dense subset
70106
diameter on a compact metric space
45581
Is the distance function in a metric space (uniformly) continuous?
128897
Bounded sequence in a metric space