For a compact and Hausdorff space X, show that the cone CX is homeomorphic to the one-point compactification of X $\times$ [0,1).
37092
Homeomorphism between a cone in a compact space and this compactification
132491
How to show that $C=C[0,1]$ is a Banach space
79213
Proof about a Topological space being arc connect
147350
Homeomorphism between $\prod X_i$ and the Cantor set
118045
Is the Baire space $\sigma$-compact?
66180
Homomorphism between compact Hausdorff spaces.
2093
If $f$ is continuous then $G$ is homeomorphic to $X$.
70082
Show: Quotient space is homeomorphic to unit sphere
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
82814
Homework question on whether two quotient spaces are homeomorphic
51914
Show that $S$ is compact.
143484
A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
93471
Space of homeomorphisms Homeo$(S^1)$ of $S^1$ deformation retracts onto $O(2)$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
143140
When are quotients of homeomorphic spaces homeomorphic?
102048
Closure of a compact set in Regular space $ X $
16228
Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism