There is no metric d,so that (Q,d) is a connected space
125580
Proving that every countable metric space is disconnected?
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
113688
Is Topological Space a Metric Space?
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
51710
Is there an infinite connected topological space such that every space obtained by removing one point from it is totally disconnected?
55263
Path connected space that is not locally connected
142503
There are no compact minimal surfaces
28804
No. of possible dense subsets of a metric space
92340
How many metrics are there on a set up to topological equivalence?
16060
Showing this metric space is complete
80274
What is the "topology induced by a metric"?
33859
How to show that a disjoint sum of metric spaces is metrizable?
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
60746
Simply connected does not imply contractible. Is there a nice counter example in $R^2$?
124688
Question about a metric on $\mathbb{R}^2$
140692
Existence of a complete metric on $(0,1)$