Image of connected set is connected implies continuity?
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
62334
Continuity and Joint Continuity
153495
Continuous function does not map closed set to closed set
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
151719
Connected set in $\mathbb{S}^1$
157384
Points of continuity is a Borel set?
108394
Proof of that every interval is connected
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
90152
Continuous with compact support implies uniform continuity
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
93623
Showing that every connected open set in a locally path connected space is path connected
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
6415
Distance function is continuous in topology induced by the metric
23225
Union of connected subsets is connected if intersection is nonempty