The Boundary of a Simply Connected Compact Set
158850
Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
89264
Connectedness in the Quotient Space
42494
The boundary is a closed set
27746
Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
55366
Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected.
92005
Existence of compact/complete metric on countable set
26919
Intersection of Connected Sets
147197
Number of connected components of the complement of a compact
49924
Analytic map with two fixed points on a simply connected domain is the identity
99236
Interior of closure of an open set
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
51914
Show that $S$ is compact.
93623
Showing that every connected open set in a locally path connected space is path connected
47056
Show that the boundary of a set equals the boundary of its complement
152442
An annulus in $\mathbb R^2$ is path connected
142901
"The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?