Compact,connected set
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
127678
A partition of the unit interval into uncountably many dense uncountable subsets
142583
Subsets of the Cantor set
55661
Existence of two disjoint closed sets with zero infimal distance
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
80180
Discrete and compact subset must be finite
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
76918
Construct a compact set of real numbers whose limit points form a countable set.
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
79531
Distance between sets with one closed set and one compact set
28391
Prove the compactness of a set B
55366
Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected.
41611
Open and closed set in n by n matrices space.
89264
Connectedness in the Quotient Space
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
74498
Smallest dense subset of $\mathbb{R}$