Mixing
Order-preserving maps
Clash Royale CLAN TAG#URR8PPP
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If I understand correctly, order-preserving maps are generally defined between reflexive, transitive, anti-symmetric relations (Posets).
Does it make sense to talk about "order-preserving maps" between reflexive and transitive relations (Quasi-orderings)? Is there an equivalent term?
order-theory
asked Jul 19 at 15:24
Matteo Corsi
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If I understand correctly, order-preserving maps are generally defined between reflexive, transitive, anti-symmetric relations (Posets).
Does it make sense to talk about "order-preserving maps" between reflexive and transitive relations (Quasi-orderings)? Is there an equivalent term?
order-theory
asked Jul 19 at 15:24
Matteo Corsi
11
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I understand correctly, order-preserving maps are generally defined between reflexive, transitive, anti-symmetric relations (Posets).
Does it make sense to talk about "order-preserving maps" between reflexive and transitive relations (Quasi-orderings)? Is there an equivalent term?
order-theory
asked Jul 19 at 15:24
Matteo Corsi
11
If I understand correctly, order-preserving maps are generally defined between reflexive, transitive, anti-symmetric relations (Posets).
Does it make sense to talk about "order-preserving maps" between reflexive and transitive relations (Quasi-orderings)? Is there an equivalent term?
order-theory
asked Jul 19 at 15:24
Matteo Corsi
11
asked Jul 19 at 15:24
Matteo Corsi
11
asked Jul 19 at 15:24
Matteo Corsi
11
asked Jul 19 at 15:24
Matteo Corsi
11
11
add a comment |Â
add a comment |Â
1 Answer
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Quasi-order preserving is fine.
Note that it makes sense to talk about a relation-preserving map between two sets endowed with arbitrary relations. That is, a map $f:Ato B$ such that $$forall x,yin A, left[xmathcalR_A yimplies f(x)mathcalR_B f(y)right]$$
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Quasi-order preserving is fine.
Note that it makes sense to talk about a relation-preserving map between two sets endowed with arbitrary relations. That is, a map $f:Ato B$ such that $$forall x,yin A, left[xmathcalR_A yimplies f(x)mathcalR_B f(y)right]$$
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
add a comment |Â
up vote
2
down vote
Quasi-order preserving is fine.
Note that it makes sense to talk about a relation-preserving map between two sets endowed with arbitrary relations. That is, a map $f:Ato B$ such that $$forall x,yin A, left[xmathcalR_A yimplies f(x)mathcalR_B f(y)right]$$
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Quasi-order preserving is fine.
Note that it makes sense to talk about a relation-preserving map between two sets endowed with arbitrary relations. That is, a map $f:Ato B$ such that $$forall x,yin A, left[xmathcalR_A yimplies f(x)mathcalR_B f(y)right]$$
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
Quasi-order preserving is fine.
Note that it makes sense to talk about a relation-preserving map between two sets endowed with arbitrary relations. That is, a map $f:Ato B$ such that $$forall x,yin A, left[xmathcalR_A yimplies f(x)mathcalR_B f(y)right]$$
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
answered Jul 19 at 15:38
Arnaud Mortier
19k22159
19k22159
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
add a comment |Â
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
Very clear, thank you very much!
– Matteo Corsi
Jul 20 at 7:56
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
@MatteoCorsi You're welcome!
– Arnaud Mortier
Jul 20 at 8:54
add a comment |Â
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