Examples of disconnected metric spaces that cannot be isometrically embedded into a connected metric space
116069
Is every metric space a subspace of some connected metric space?
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
66550
Cardinality of separable metric spaces
17607
Open maps which are not continuous
109638
Show that a complete metric space without isolated points is uncountable
19984
Example of topological spaces with continuous bijections that are not homotopy equivalent
128897
Bounded sequence in a metric space
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
65180
A compact Hausdorff space that is not metrizable
80274
What is the "topology induced by a metric"?
126759
Unbounded continuous function on non-compact metric space
133938
Connectedness of the Hausdorff distance.
60746
Simply connected does not imply contractible. Is there a nice counter example in $R^2$?
127166
Specific example of a space that is separable but not second countable.
106298
Prove that some topology is not metrizable