Quotient topology $\mathbb{R}/\sim $ where $x\sim y$ iff $x-y\in\mathbb{Z}$
60981
Understanding relation between Quotient Space and $S^1$
109764
Find the cardinality of the quotient of $\mathbb R$ in respect to R
78006
What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
122958
$R/I$ is commutative iff $rs-sr \in I$
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
99353
Topology on cartesian product and product topology.
79236
Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)
18828
Base and empty set of a topology
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
32205
Topology on the real numbers such that all polynomials are continuous but cosine is not continuous
152679
Homogeneous topological spaces
147752
Is the quotient map a homotopy equivalence?
6118
Homeomorphism of the real line-Topology
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
12104
How to prove this result involving the quotient maps and connectedness?