Is there a general term for a mapping of a set to itself?

Asked May 16 '19 at 15:17

Active May 16 '19 at 15:17

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I often wish to describe a mapping of a set to itself as injective, or bijective, etc. The sentence $f$ is an injective mapping of the set $\mathcal{A}$ into itself seems unnecessarily wordy. I would like to say something like: $f$ is an injective endomapping of the set $\mathcal{A}.$ Where I have coined the term endomapping to mean the mapping of a set to itself.

Is there an established mathematical term for this?

asked May 16 '19 at 15:17

Steven Thomas Hatton

3,353

There is nothing wrong with your first version: everyone would understand it. One could argue your second version is unnecessarily high-falutin'. – Randall May 16 '19 at 15:21
1

self-map is sometimes used. – Dave L. Renfro May 16 '19 at 15:23
it's called a self-map – user29418 May 16 '19 at 15:23
@user29418 that would make Fowler and Fowler happy. "Prefer the Saxon word." – Steven Thomas Hatton May 16 '19 at 15:26
"Endomap" and "endofunction" work but are IMO slightly awkward. I don't really know a non-awkward term. – Qiaochu Yuan May 16 '19 at 16:54

Is there a general term for a mapping of a set to itself?

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