Characterizing the Homotopy of Path-Connected Space
126881
(weak) homotopy equivalence
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
4462
Homotopy invariance for cohomology
95187
The set of homotopy classes
120100
Hairy Ball Theorem: homotopy from the identity to the antipodal map
114990
Is the complement of countably many disjoint closed disks path connected?
156904
Homotopy Extension Property: necessary and sufficient condition
142698
Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
72556
Is the closure of path-connected set path connected?
135783
Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected?
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
13468
When does open and connected imply path-connected?
23156
Homotopy equivalence from torus minus a point to a figure-eight.
151581
Prerequisite for Milnor Topology from a Differential Viewpoint
10215
Differentiable manifolds as locally ringed spaces
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
35069
Connectedness of the boundary