# Category:Quotient Mappings

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This category contains results about **Quotient Mappings**.

Definitions specific to this category can be found in Definitions/Quotient Mappings.

Let $\RR \subseteq S \times S$ be an equivalence on a set $S$.

Let $\eqclass s \RR$ be the $\RR$-equivalence class of $s$.

Let $S / \RR$ be the quotient set of $S$ determined by $\RR$.

Then $q_\RR: S \to S / \RR$ is the **quotient mapping induced by $\RR$**, and is defined as:

- $q_\RR: S \to S / \RR: \map {q_\RR} s = \eqclass s \RR$

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Quotient Mappings"

The following 20 pages are in this category, out of 20 total.

### C

- Composite of Quotient Mappings
- Condition for Mapping from Quotient Set to be Injection
- Condition for Mapping from Quotient Set to be Surjection
- Condition for Mapping from Quotient Set to be Well-Defined
- Conditions for Commutative Diagram on Quotient Mappings between Mappings
- Construction of Inverse Completion

### Q

- Quotient Mapping is Bounded in Normed Quotient Vector Space
- Quotient Mapping is Coequalizer
- Quotient Mapping is Surjection
- Quotient Mapping Maps Unit Open Ball in Normed Vector Space to Unit Open Ball in Normed Quotient Vector Space
- Quotient Mapping on Structure is Epimorphism
- Quotient Theorem for Sets
- Quotient Theorem for Surjections