If $M$ is a nonorientable $3$-manifold, why is $H_1(M, \mathbb{Z})$ infinite?
108106
If M is a non-orientable closed connected 3 manifold prove H1(M) is an infinite group.
94018
Homology groups of $\mathbb{R}^3\setminus \ S^1$ and $\mathbb{R}^3\setminus E^1_+$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
152725
Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
78963
Homotopy lifting property of $\mathbb{R} \to S^1$ in Hatcher
62766
Topological Manifolds & Covers
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
92504
Criteria of a trivial G bundle of a 3-manifold
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
149029
3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
76937
Is there an elementary way to see that there is only one complex manifold structure on $R^2$?
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
68234
Is $[0,1) \cup \{2\}$ a manifold with boundary? My issue is the $2$.
95867
Subgroup of $C^*$ (nonzero complex) with finite index.
36519
Explicit example of a compact manifold of dimension $>2$ with strictly negative sectional curvature