I am new in topological algebra however, I know an example of a space X which has just one point $x_{0}\ \in\ X $ that $x_{0}$ is a deformation retraction of X:
A cone CQ wich Q is rational number set, is just have one deformation retract point and its the vertex point $x_{0}$.
deformation retraction:
A continuous map
$F:X \times [0,1] \rightarrow X$
is a deformation retraction of a space X onto a subspace A if, for every x in X and a in A,
$F(x,0)=x,\ F(x,1)\ \in \ A\ and\ F(a,1)=a$
The subspace A is called a deformation retract of X.
Contractible space
a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is one that can be continuously shrunk to a point within that space.
my question is: I need an example of a topological space which is contractible but has no point to be its deformation retraction.