Simply connected domain (Homotopy)
70538
Intersection and union of simply connected domain
131890
Totally disconnected space that is not $T_2$
94215
Fundamental group of the connected sum of manifolds
102323
Nice neighborhoods of each "piece" in a manifold connected sum
89264
Connectedness in the Quotient Space
95187
The set of homotopy classes
32923
Homotopy equivalence of universal cover
147752
Is the quotient map a homotopy equivalence?
120100
Hairy Ball Theorem: homotopy from the identity to the antipodal map
35069
Connectedness of the boundary
158850
Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
102914
Integral domain that is not a factorization domain
135863
Is the graph of a continuous function homeomorphic to its domain?
100437
Classification of connected subsets of the real line (up to homeomorphism)
151051
connectedness of uniform topology
141078
Domain over which a polynomial is strictly positive
129943
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$