# Category:Identity Mappings

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

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

The **identity mapping** of a set $S$ is the self-map $I_S: S \to S$ defined as:

- $I_S = \set {\tuple {x, y} \in S \times S: x = y}$

or alternatively:

- $I_S = \set {\tuple {x, x}: x \in S}$

That is:

- $I_S: S \to S: \forall x \in S: \map {I_S} x = x$

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### F

### I

## Pages in category "Identity Mappings"

The following 47 pages are in this category, out of 47 total.

### C

### D

### I

- Identity Function is Completely Multiplicative
- Identity Function is Odd Function
- Identity Mapping between Metrics separated by Scale Factor is Continuous
- Identity Mapping is Automorphism
- Identity Mapping is Automorphism/Groups
- Identity Mapping is Automorphism/Ordered Semigroups
- Identity Mapping is Automorphism/Rings
- Identity Mapping is Automorphism/Semigroups
- Identity Mapping is Bijection
- Identity Mapping is Continuous
- Identity Mapping is Homeomorphism
- Identity Mapping is Idempotent
- Identity Mapping is Injection
- Identity Mapping is Left Identity
- Identity Mapping is Order Isomorphism
- Identity Mapping is Ordered Ring Automorphism
- Identity Mapping is Ordered Semigroup Automorphism
- Identity Mapping is Permutation
- Identity Mapping is Relation Isomorphism
- Identity Mapping is Right Identity
- Identity Mapping is Surjection
- Identity Mapping on Metric Space is Homeomorphism
- Identity Mapping on Real Vector Space from Chebyshev to Euclidean Metric is Continuous
- Identity Mapping on Real Vector Space from Euclidean to Chebyshev Distance is Continuous
- Identity Mapping on Symmetric Group is Even Permutation
- Identity Mapping to Coarser Topology is Continuous
- Identity Mapping to Expansion is Closed
- Identity Permutation is Disjoint from All
- Inclusion Mapping is Restriction of Identity
- Inclusion Mapping is Surjection iff Identity
- Inverse of Identity Mapping