# Category:Bijections

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This category contains results about **Bijections**.

Definitions specific to this category can be found in Definitions/Bijections.

A mapping $f: S \to T$ is a **bijection** if and only if both:

- $(1): \quad f$ is an injection

and:

- $(2): \quad f$ is a surjection.

## Also see

## Subcategories

This category has the following 18 subcategories, out of 18 total.

### B

### C

### E

### H

### I

### L

### R

## Pages in category "Bijections"

The following 62 pages are in this category, out of 62 total.

### B

- Bijection between Specific Elements
- Bijection from Cartesian Product of Initial Segments to Initial Segment
- Bijection has Left and Right Inverse
- Bijection iff exists Mapping which is Left and Right Inverse
- Bijection iff Left and Right Cancellable
- Bijection iff Left and Right Inverse
- Bijection iff Left and Right Inverse/Corollary
- Bijection is Open iff Closed
- Bijection on Total Ordering is Order Isomorphism
- Bijection on Total Ordering reflects Total Ordering
- Bijection Preserves Set Partition
- Bijective Continuous Linear Operator is not necessarily Invertible
- Bijective Relation has Left and Right Inverse

### C

- Cantor-Bernstein-Schröder Theorem
- Cardinality of Set of Bijections
- Cardinality of Surjection
- Cartesian Product of Bijections is Bijection
- Cartesian Product of Bijections is Bijection/General Result
- Codomain of Bijection is Domain of Inverse
- Composite of Bijection with Inverse is Identity Mapping
- Composite of Bijections is Bijection
- Composite of Three Mappings in Cycle forming Injections and Surjection
- Composition of 3 Mappings where Pairs of Mappings are Bijections
- Composition of Three Mappings which form Identity Mapping
- Continuous Real Function on Closed Interval is Bijective iff Strictly Monotone

### D

### E

### I

- Identity Mapping is Bijection
- Image of Relative Complement under Bijection is Relative Complement of Image
- Injection is Bijection iff Inverse is Injection
- Injection to Image is Bijection
- Integer Power Function is Bijective iff Index is Odd
- Inverse Element of Bijection
- Inverse Mapping is Bijection
- Inverse of Bijection is Bijection
- Inverse of Composite Bijection
- Inverse of Increasing Bijection need not be Increasing
- Inverse of Inverse of Bijection
- Inverse Relation is Left and Right Inverse iff Bijection
- Invertible Continuous Linear Operator is Bijective