I see the definition in book which tells that: If we say linear space $A$ is embedding in $B$, it means $A$ is contained in $B$ and the mapping $A\to B$ is continuous.
But I also see the definition in wiki which tells that: the mapping $A\to B$ is injective.
What is exactly the definition of embedding? I'm confused of it. Thank you!
If $A$ is contained in $B$, then the mapping $$ f:A\to B,\qquad a\mapsto a $$ will always be injective.
As for the definition of embedding, there are variants: some require that $f$ is continuous, and some do not require this property. In the latter case, they use the term "continuous embedding" to denote the case that $f$ is continuous.