Is there a metric on the reals $\Bbb R$ so that a subset of $\Bbb R$ is open iff its complement is finite?
39010
Metrization of the cofinite topology
45405
An elementary way to show any bounded subset of $\Bbb{R}^k$ is totally bounded
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
137881
A not complete metric space?
109046
Is the complement of an open ball in a Banach space connected?
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
13848
Showing that if a subset of a complete metric space is closed, it is also complete
70264
Prove that the inverse image of an open set is open
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
27855
Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
15480
Open set in a metric space is union of closed sets