Recall that a triple $(X,\tau,\ast)$ is a right topological semigroup if for every $x,y,z\in X$ it stands that $(x\ast y)\ast z=x\ast(y\ast z)$ and for every $y\in X$ we have that the map $\ast_y:X\to X$ given by $\ast_y(x)=x\ast y$ is $\tau$-continuous.
It's known that given a set $X$ there exist a map $f:X^2\to X$ such that $(X,f)$ is a group, but is not truth that given a topological space $(X,\tau)$ exists a map $f:X^2\to X$ such that $(X,\tau,f)$ is a topological group, even if $X$ is a compact Hausdorff space.
My question is: It's truth that every topological space admits a right topological semigroup structure?
Yes. Let $(X,\tau)$ be any topological space. For $x,y\in X$ define $f(x,y)=x$ and $g(x,y)=y.$ Then $(X,\tau,f)$ and $(X,\tau,g)$ are topological semigroups.