Let X and Y be normed spaces. What will be the dual space of $X\cap Y$? We consider the norm on $X\cap Y$ to be the sum norm $\norm[x]=\norm[x]_X+\norm[x]_Y$.
Is your question more about computer programming, intersectionality(social sciences), or something else? My most recent book on social scientific intersectionality: Book Respectfully and Unfortunately, The Improbability of, and Da...