Let $X$ a topological vector space. We know that the weak topology $\sigma(X,X^*)$ is the weakest locally convex topology in $X$ that make every $f \in X^*$ continuous. Consequently, if $\tau$ is the topology of $X$, $\sigma(X,X^*)\subset \tau.$ Does something similar happen with the strong topology $\beta(X,X^*)?$
When we consider the definition of reflexive space, we topologize $X^*$ with $\beta(X^*,X),$ but I'd like to know the reason of that.

Let $X$ be a topological vector space. We know that the weak topology $\sigma(X,X^*)$ is the weakest locally convex topology in $X$ that make every $f \in X^*$ continuous. Consequently, if $\tau$ is the topology of $X$, $\sigma(X,X^*)\subset \tau.$ Does something similar happen with the strong topology $\beta(X,X^*)?$
When we consider the definition of reflexive space, we topologize $X^*$ with $\beta(X^*,X),$ but I'd like to know the reason of that.

Let $X$ a TVS. We know that the weak topology $\sigma(X,X^*)$ is the weakest localy convex topology in $X$ that make every $f \in X^*$ continuous. Consequently, if $\tau$ is the topology of $X$, $\sigma(X,X^*)\subset \tau.$ Does something similar happen with the strong topology $\beta(X,X^*)?$
When we consider the definition of Reflexive Space, we topologize $X^*$ with $\beta(X^*,X),$ but I'd like to know the reason of that.

Let $X$ a topological vector space. We know that the weak topology $\sigma(X,X^*)$ is the weakest locally convex topology in $X$ that make every $f \in X^*$ continuous. Consequently, if $\tau$ is the topology of $X$, $\sigma(X,X^*)\subset \tau.$ Does something similar happen with the strong topology $\beta(X,X^*)?$
When we consider the definition of reflexive space, we topologize $X^*$ with $\beta(X^*,X),$ but I'd like to know the reason of that.