$\mathbb{R},\emptyset$, and every interval $(-n,n)$ are a topology
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
41047
Subspace Topology of a subset
53850
Proof that every normed vector space is a topological vector space
31617
Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
72190
Topological proof on discrete topology where $X$ is infinite
156783
$\mathbb R$ has the same cardinality of any interval
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
82628
Cardinality of a set of closed intervals
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
40071
What is the cardinality of the set of all topologies on $\mathbb{R}$?
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
133820
The product topology on $\mathbb R_d\times \mathbb R$ vs. the dictionary order topology on $\mathbb R\times \mathbb R$
95747
Number of countable subsets of $\mathbb{R}$
61375
Meaning of $\mathbb{R}[x]$
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?