# Category:Constant Mappings

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

A **constant mapping** or **constant function** is a mapping $f_c: S \to T$ defined as:

- $c \in T: f_c: S \to T: \forall x \in S: \map {f_c} x = c$

That is, every element of $S$ is mapped to the same element $c$ in $T$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Constant Mappings"

The following 25 pages are in this category, out of 25 total.

### C

- Composite with Constant Mapping is Constant Mapping
- Constant Function is Continuous
- Constant Function is Continuous/Metric Space
- Constant Function is Continuous/Metric Space/Proof 1
- Constant Function is Continuous/Metric Space/Proof 2
- Constant Function is Continuous/Real Function
- Constant Function is Primitive Recursive
- Constant Function is Primitive Recursive/General Case
- Constant Function is Uniformly Continuous
- Constant Function is Uniformly Continuous/Metric Space
- Constant Function is Uniformly Continuous/Real Function
- Constant Mapping is Continuous
- Constant Mapping is Non-Commutative
- Constant Mapping to Group Identity is Homomorphism
- Constant Mapping to Identity is Homomorphism
- Constant Real Function is Absolutely Continuous
- Constant Real Function is Continuous
- Continuous Real-Valued Function on Irreducible Space is Constant