Which of spaces \(X\) and \(Y\) are homeomorphic:

(1) \(X= \mathbb{R}\) and \(Y=[0,1)\)

(2) \(X=\mathbb{R}\) and \(Y=[0,1]\)

(3) \(X=[1, \infty)\) and \(Y=(0,1]\)

(4) \(X=\mathbb{R}\) and \(Y=(0,1)\)

(5) \(X=\mathbb{Q}\) and \(Y=\mathbb{Q}\)

(6) \(X=\{(x,y,z) \in \mathbb{R^3} : x^2+y^2 =z ,r<z<R \}\) and \(Y =A(0,r,R)\)

(7) \(X= \{x \in \mathbb{R^{n+1}}:x_{n+1}=0 \}\) and \(Y= \mathbb{R^n}\)

- Voclasses