Answer to Question #141631 in Differential Geometry | Topology for Orif

Question

A set S is cardinally majorizable by a set T iff there exists a(n) ______________ from T to S.

It is not injection. Bijection from T to S? Maybe so that there will be injection from S to T.

Answer 1

A map $f: X \to Y$ is called a surjection if for each $y\in Y$ there exists $x\in X$ such that $f(x)=y.$

A set $S$ is cardinally majorizable by a set $T$ iff there exists a surjection from $T$ to $S$.

As bonus for the customer note that if $f: T\to S$ is a surjection, then we can construct an injection $g: S\to T$ in the following way: for each $s\in S$ choose exactly one element $t\in f^{-1}(s)\ne\emptyset$, and define $g(s)=t$. Since $f^{-1}(s_1)\cap f^{-1}(s_2)=\emptyset$ for $s_1\ne s_2$, $g$ is an injection.