The converse of continuous image of a connected set is connected
17607
Open maps which are not continuous
70264
Prove that the inverse image of an open set is open
85175
Continuous Images of $GL_n(\mathbb{R})$
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
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 $X\times Y$
122086
continuous function: preimage of closure of a set is closure of preimage
70645
Borel set preserved by continuous map
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
130156
Image of the union and intersection of sets.
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
48764
Increasing real valued function whose image set is connected
3649
Closed unit interval is connected proof
140929
Increasing, continuous function implies connectivity and viceversa.
48557
Product of connected spaces
26794
Metrizability of Hausdorff continuous image of compact metric space
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
151719
Connected set in $\mathbb{S}^1$