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.

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 …

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 10, 2013 · 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.

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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 …

So it is basically counting the number of different ways the elements of set A can map to elements of B such that each element of B has something from A mapping to it - thus this mapping …

Aug 4, 2019 · And a split surjection? I am aware of the definitions of split monomorphism and split epimorphism in an arbitrary category. However, is there a more intuitive definition of split …

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.

Feb 29, 2024 · Yes, you're right. In fact, the converse also holds: if a function satisfies the condition you mentioned, it is surjective.