Category:Definitions/Increasing Mappings
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This category contains definitions related to Increasing Mappings.
Related results can be found in Category:Increasing Mappings.
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.
Let $\phi: S \to T$ be a mapping.
Then $\phi$ is increasing if and only if:
- $\forall x, y \in S: x \preceq_1 y \implies \map \phi x \preceq_2 \map \phi y$
Note that this definition also holds if $S = T$.
Also see
Subcategories
This category has the following 2 subcategories, out of 2 total.
I
- Definitions/Increasing Sequences (19 P)
O
Pages in category "Definitions/Increasing Mappings"
The following 16 pages are in this category, out of 16 total.
I
- Definition:Increasing
- Definition:Increasing Function
- Definition:Increasing Mapping
- Definition:Increasing Mapping/Also known as
- Definition:Increasing Real Function
- Definition:Increasing Real Function/Also known as
- Definition:Increasing/Mapping
- Definition:Increasing/Real Function
- Definition:Increasing/Sequence
- Definition:Isotone Mapping