Jan 11, 2018 · I think the definition of a surjection is pretty clear in that each element of x is mapped to some value of y. But I'm a little confused about the difference between an injection …

I usually use two types of notations for function, injection, surjection and bijiection as follows. Note that the \twoheadrightarrowtail is defined as follows, and the others are AMS symbols.

26 Can anyone give me a good explanation of how and why words surjection and injection came into use in mathematical community? What do they exactly mean? Who introduced them? I …

Apr 6, 2014 · What are some mnemonics to help one remember that Injection = One-to-one and Surjection = Onto? The only thing I can think of is 1njection = 1-1.

Jul 27, 2024 · Note that the closed map lemma cannot be generalised, for example $ (0,1)\to [0,1]$ is not closed. So there might exist continuous surjection from locally compact space to …

4 Cantor-Bernstein-Schroeder Theorem And the fact that, if there exists a surjection from A to B, then there exists an injection from B to A.

Yes, there exists a continuous surjection from $\mathbb R$ to $\mathbb R^2$. The following is a simple way to construct one, although there should be more elegant constructions.

If there exists a surjection from $Y$ onto $X$ then there exists an injection from $X$ into $Y$ It is still open whether or not the partition principle implies the axiom of choice, so it might be …

I hope you're good and healthy man, it's been 8 years since you used stackexchange so hope you are well and happy!

Feb 29, 2024 · Yes, I see clearly (and hopefully correct) that the preimage of the image of a set is that same set if the function is an injection (surjection is not required).