Example for connected set
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
15160
Example of Riemann integrable $f: [0,1] \to \mathbb R $ whose set of discontinuity points is an uncountable and dense set in $[0,1]$
108394
Proof of that every interval is connected
109229
An Example of a Nested Decreasing Sequence of Bounded Closed Sets with Empty Intersection
39382
Examples of the Pigeonhole Principle
72213
Can a $N-1$ rectifiable set be partitioned into countably many connected pieces?
10541
How to prove Mandelbrot set is simply connected?
89264
Connectedness in the Quotient Space
63701
An example of a regular function over an open set
84791
Is every connected metric space with at least two points uncountable?
130156
Image of the union and intersection of sets.
129227
An example of neither open nor closed set
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
80524
Path-connected and locally connected space that is not locally path-connected
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
2575
Showing that $\mathbb{R}$ is connected
147961
Characterizing simply connected spaces