Connected implies continuity
77621
Continuity of function mapping connected set to connected set
60383
What is the intuition for the point-set topology definition of continuity?
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
150554
proof that $f'$ is continuous at $a$
18039
Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
151923
$F$ closed and connected then...
53738
Monotone functions and continuity
124234
Prove that if $X$ and it's closure $\overline X$ are connected and if $X\subset Y \subset \overline X$, show that Y is also connected.
15487
Continuous function from a connected set?
64619
Continuity of a function of product spaces
6415
Distance function is continuous in topology induced by the metric
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
58631
Continuity and the Axiom of Choice
23225
Union of connected subsets is connected if intersection is nonempty
122086
continuous function: preimage of closure of a set is closure of preimage