Show that no two of the spaces $(0,1), \ (0, 1], \ [0,1]$ are homeomorphic.
52012
Is there exist a homemoorphism between either pair of $(0,1),(0,1],[0,1]$
55374
Cover of (0,1) with no finite subcover & Open sets of compact function spaces
36315
Is $[0,1]$ a countable disjoint union of closed sets?
93389
Uncountable sets of Hausdorff dimension zero
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
20383
True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$
45216
Cardinality of $[0,1]$
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
92774
Prove that a linear subspace of $C([0,1])$ is closed
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
81264
Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
112306
Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic
84707
How to prove a cross is not locally homeomorphic to an euclidean space?
102250
Subset of $C[0,1]$ is nowhere dense