Inclusion

Redirect to:

• Relative topology#New maps

Given a set X and another set $Y$ all elements of which also belong to $X$. Then $Y$ is called a subset of $X$. The function $i_Y: Y → X$ given by $i_Y(x) = x$ is called the inclusion.

A trivial function but there are issues to discuss:

• What if X is a topological space? Is the inclusion always continuous?
• What if X is a group? What is the right question to ask?

Inclusion is a restriction of the identity function to a subset.