Metric space compactness
55337
Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.
84791
Is every connected metric space with at least two points uncountable?
145415
Examples of almost compact spaces.
126759
Unbounded continuous function on non-compact metric space
116069
Is every metric space a subspace of some connected metric space?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
70106
diameter on a compact metric space
18040
Show that a compact metric space is bounded
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
83159
Defining a metric space
152493
Is an expanding map on a compact metric space continuous?
132641
Proving that Euclidean Space is a complete metric space
74877
Every metric space with a countable base is separable
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
84004
Prove there is no contraction mapping from compact metric space onto itself
157753
Show that any set in a metric space can be written as the intersection of open sets