Is $( \mathbb{R} , T)$ connected if T is finite complement topology on $\mathbb{R}$
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
137621
The Number of Topologies on a Finite Set
50966
In a topological space, why the intersection only has to be finite?
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
84492
Can $X$ have compact connected components?
39010
Metrization of the cofinite topology
66334
How is every subset of the set of reals with the finite complement topology compact?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
59531
Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
100437
Classification of connected subsets of the real line (up to homeomorphism)
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
135783
Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected?
35069
Connectedness of the boundary
77621
Continuity of function mapping connected set to connected set
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected