Canonical projection of an equivalence relation

From Maths
Revision as of 22:33, 8 October 2016 by Alec (Talk | contribs) (Created page with "{{Stub page|grade=D|msg=This page is of low priority. Those looking for information should visit equivalence relation instead. It should be expanded though!}} __TOC__ ==De...")

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
Stub grade: D
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
This page is of low priority. Those looking for information should visit equivalence relation instead. It should be expanded though!

Definition

Let [ilmath]X[/ilmath] be a set and [ilmath]\sim\subseteq X\times X[/ilmath] an equivalence relation on [ilmath]X[/ilmath]. Then the map:

  • [ilmath]\pi:X\rightarrow X/\sim[/ilmath] given by [ilmath]\pi:x\mapsto [x][/ilmath] (where [ilmath][x][/ilmath] denotes the equivalence class of [ilmath]x[/ilmath]) is a function.

We call this map the "canonical projection of the equivalence relation", sometimes just the "canonical map of the equivalence relation" for short.

References