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

I am a 9th grader self-studying about set theory and functions. I understood most basic concepts, but I didn't understand what is a surjective function. I have understood what is an injective funct...

Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is …

Jun 16, 2017 · Whether or not a function like that is surjective becomes an interesting question, not only for solving equations, but for answering other questions about the structure of the …

Apr 11, 2023 · Is the function surjective, injective or bijective?". My (simplified) understanding of a injective function is that every value for X has to map to a unique value on Y.

Oct 24, 2020 · For Banach spaces $X$ and $Y$, a bounded operator $A: X\to Y$ is also bounded below iff the adjoint $A^*: Y^*\to X^*$, defined as $A^*: f\mapsto f\circ A$, is surjective.

Here you don't care about domains and codomains. This is often good enough for practical considerations. But from the formal viewpoint, it doesn't make sense to ask whether this …

For one, you can talk about a function being surjective if the domain and codomain are simply sets, but you cannot talk about a function being continuous unless the domain and codomain …

I have the same feeling as yours: often, proving that a linear map is injective is easier than proving it is surjective. Of course we are talking about infinite-dimensional vector spaces, otherwise …

Jan 11, 2021 · A surjective, continuous and closed map is a quotient map Ask Question Asked 4 years, 10 months ago Modified 4 years, 10 months ago