A question about the projection function

Question

Let $p:A\times B\to. A$

$p(x,y)=x$

The projection function $p$ is clearly subjective. I want to know if it is bijective? The projective function suspiciously looks like $1_A(x)=x$

I corrected my mistake. It should be A – Jul 28 '20 at 12:57 — , Jul 28 '20 at 12:57

score 2 · Answer 1 · answered Jul 28 '20 at 12:47

2

If $|A|>1$ then we have two $a\ne a'$.

Since $p(a,x) = p(a',x)=x$ we see it is not injective and so it is...?

answered Jul 28 '20 at 12:47

User2020201

It is not bijective and can’t be an isomorphism .If it was I could use it in a theorem – Jul 28 '20 at 12:58

1 Answers1