If $X$ is a metric space such that any metric space $Y$ , which is a homeomorphic image of $X$ , is complete , then is $X$ compact?
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
77563
Homeomorphism between spaces equipped with cofinite topologies
20383
True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
70106
diameter on a compact metric space
58948
If $A$ is compact, is then $f(A)$ compact?
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
69528
Metrizability of quotient spaces of metric spaces
100560
$X$ compact Hausdorff space, characterize the maximal ideals of $C(X)$
90628
The metric spaces are Tychonoff spaces
84791
Is every connected metric space with at least two points uncountable?
149220
If every compact set is closed, then is the space Hausdorff?
70017
Every subspace of a compact space is compact?
13848
Showing that if a subset of a complete metric space is closed, it is also complete