# Definition:Mapping/Also known as

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## Definition

Words which are often used to mean the same thing as **mapping** include:

**transformation**(particularly in the context of self-maps)**operator**or**operation****function**(usually in the context of numbers)**map**(but this term is discouraged, as the term is also used by some writers for**planar graph**).

Some sources introduce the concept with informal words such as **rule** or **idea** or **mathematical notion**.

Sources which define a **mapping (function)** to be only a many-to-one relation refer to a **mapping (function)** as a **total mapping (total function)**.

Some use the term **single-valued relation**.

Sources which go into analysis of multifunctions often refer to a conventional **mapping** as:

- a
**single-valued mapping**or**single-valued function** - a
**many-to-one mapping**,**many-to-one transformation**, or**many-to-one correspondence**, and so on.

The wording can vary, for example: **many-one** can be seen for **many-to-one**.

A **mapping $f$ from $S$ to $T$** is also described as a **mapping on $S$ into $T$**.

In the context of class theory, a **mapping** is often seen referred to as a **class mapping**.

## Sources

- 1955: John L. Kelley:
*General Topology*... (previous) ... (next): Chapter $0$: Functions - 1959: E.M. Patterson:
*Topology*(2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Topological Spaces: $\S 9$. Functions - 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 4$. Relations; functional relations; mappings:*Remark $1$* - 1975: Bert Mendelson:
*Introduction to Topology*(3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 6$: Functions - 1978: John S. Rose:
*A Course on Group Theory*... (previous) ... (next): $0$: Some Conventions and some Basic Facts - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 20$: Remarks - 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 9$ Functions