Category:Progressing Mappings
This category contains results about Progressing Mappings.
Definitions specific to this category can be found in Definitions/Progressing Mappings.
Let $C$ be a class.
Let $f: C \to C$ be a mapping from $C$ to $C$.
Then $f$ is a progressing mapping if and only if:
- $x \in C \implies x \subseteq \map f x$
That is, if and only if for each $x \in C$, $x$ is a subset of $\map f x$.
Also known as
A progressing mapping is also known as an inflationary mapping, which is the term generally used in the context of an arbitrary ordered structure, notably in the field of measure theory.
Some sources use the term progressive mapping.
The term extensive mapping can also occasionally be seen, but this is not endorsed on $\mathsf{Pr} \infty \mathsf{fWiki}$ because of its possible confusion with the concept of the Axiom of Extensionality.
Sources which prefer the term function to mapping will tend to use such here: progressing function, inflationary function, and so on.
Subcategories
This category has the following 14 subcategories, out of 14 total.
Pages in category "Progressing Mappings"
The following 17 pages are in this category, out of 17 total.
C
M
N
S
- Sandwich Principle for Minimally Closed Class
- Set of Subsets of Element of Minimally Inductive Class under Progressing Mapping is Finite
- Set which is Superinductive under Progressing Mapping has Fixed Point
- Set which is Superinductive under Progressing Mapping has Fixed Point/Corollary
- Successor Mapping is Progressing
- Successor Mapping on Natural Numbers is Progressing