Timeline for Request for literature recommendations on isotonic mappings
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2023 at 9:49 | comment | added | user178594 | See my answer for more details. | |
| Mar 21, 2023 at 9:21 | answer | added | user178594 | timeline score: 1 | |
| Mar 19, 2023 at 10:55 | comment | added | Michael Greinecker | Every function $f:X\to Y$ satisfies that $A\subseteq B$ implies $f(A)\subseteq f(B)$ without any further condition. | |
| Mar 19, 2023 at 10:38 | comment | added | stalinon | @MichaelGreinecker Generalized isotonic mappings of sets are functions that preserve the order of sets, but they also allow the possibility of incomparability. More formally, a function f: X → Y is isotonic if for any subsets A, B of X, if A ⊆ B and there is no x in A and y in B such that x is not comparable to y, then f(A) ⊆ f(B). | |
| Mar 19, 2023 at 10:36 | comment | added | stalinon | @YCor I used a more general term due to my own inexperience. studying mathematics in my undergraduate degree, I did not come across such terms even in my native language, and my technical English is not good enough for a correct translation. Sorry about that, "isotonic maps between posets" is indeed more correct | |
| Mar 19, 2023 at 10:33 | comment | added | Michael Greinecker | That leaves open the question of what you mean by generalized isotonic mappings. | |
| Mar 19, 2023 at 10:27 | comment | added | YCor | I've added the definition in the post and edited the tags. I guess this is also sometimes called "order-preserving" and has several other names. I'm not sure "isotonic maps of sets" makes sense, why not "isotonic maps between posets"? | |
| Mar 19, 2023 at 10:22 | history | edited | YCor | CC BY-SA 4.0 |
edited tags, added definition
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| Mar 19, 2023 at 10:21 | comment | added | stalinon | @YCor An isotonic mapping is a function between two partially ordered sets that preserves the ordering between the elements. Specifically, given two partially ordered sets (X, ≤) and (Y, ≤), a function f: X → Y is isotonic if for any x, y ∈ X such that x ≤ y, it is true that f(x) ≤ f(y). | |
| Mar 18, 2023 at 22:56 | comment | added | Michael Greinecker | Lattice programming? | |
| Mar 18, 2023 at 15:01 | review | Close votes | |||
| Apr 2, 2023 at 3:02 | |||||
| Mar 18, 2023 at 14:45 | comment | added | kjetil b halvorsen | This is the context in which I know isotonic, yours must be different? | |
| Mar 18, 2023 at 14:38 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 18, 2023 at 14:37 | comment | added | YCor | Could you provide at least one link using this terminology? The links I've found are totally unrelated to set theory. | |
| S Mar 18, 2023 at 14:34 | review | First questions | |||
| Mar 18, 2023 at 14:45 | |||||
| S Mar 18, 2023 at 14:34 | history | asked | stalinon | CC BY-SA 4.0 |