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Sets equipped with sublattice of their power sets
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Topology and measure theory are two examples of fields which include, in their objects of study, sets which are given structure by equipping them with a lattice of a certain type sitting in their power set. Are there other examples of this pattern?
general-topology measure-theory lattice-orders
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
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add a comment |
$begingroup$
Topology and measure theory are two examples of fields which include, in their objects of study, sets which are given structure by equipping them with a lattice of a certain type sitting in their power set. Are there other examples of this pattern?
general-topology measure-theory lattice-orders
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
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1
$begingroup$
See field of sets
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– mrp
Mar 13 at 7:50
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Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
Mar 14 at 3:01
add a comment |
$begingroup$
Topology and measure theory are two examples of fields which include, in their objects of study, sets which are given structure by equipping them with a lattice of a certain type sitting in their power set. Are there other examples of this pattern?
general-topology measure-theory lattice-orders
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
$endgroup$
Topology and measure theory are two examples of fields which include, in their objects of study, sets which are given structure by equipping them with a lattice of a certain type sitting in their power set. Are there other examples of this pattern?
general-topology measure-theory lattice-orders
general-topology measure-theory lattice-orders
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
asked Mar 13 at 6:45
David FarrellDavid Farrell
161
161
1
$begingroup$
See field of sets
$endgroup$
– mrp
Mar 13 at 7:50
$begingroup$
Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
Mar 14 at 3:01
add a comment |
1
$begingroup$
See field of sets
$endgroup$
– mrp
Mar 13 at 7:50
$begingroup$
Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
Mar 14 at 3:01
1
1
$begingroup$
See field of sets
$endgroup$
– mrp
Mar 13 at 7:50
$begingroup$
See field of sets
$endgroup$
– mrp
Mar 13 at 7:50
$begingroup$
Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
Mar 14 at 3:01
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Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
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A bornology is an example too.
A convexity structure is not a lattice (not closed under unions, just under
intersections and directed unions), but does have the "feel" of a topological structure, to me at least.
A convergence space is a set $X$ and a relation on the set of ultrafilters on it times $X$, etc. So such "second order" (or higher order) structures are not uncommon. Not always lattice based, though.
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
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$begingroup$
A bornology is an example too.
A convexity structure is not a lattice (not closed under unions, just under
intersections and directed unions), but does have the "feel" of a topological structure, to me at least.
A convergence space is a set $X$ and a relation on the set of ultrafilters on it times $X$, etc. So such "second order" (or higher order) structures are not uncommon. Not always lattice based, though.
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
$endgroup$
add a comment |
$begingroup$
A bornology is an example too.
A convexity structure is not a lattice (not closed under unions, just under
intersections and directed unions), but does have the "feel" of a topological structure, to me at least.
A convergence space is a set $X$ and a relation on the set of ultrafilters on it times $X$, etc. So such "second order" (or higher order) structures are not uncommon. Not always lattice based, though.
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
$endgroup$
add a comment |
$begingroup$
A bornology is an example too.
A convexity structure is not a lattice (not closed under unions, just under
intersections and directed unions), but does have the "feel" of a topological structure, to me at least.
A convergence space is a set $X$ and a relation on the set of ultrafilters on it times $X$, etc. So such "second order" (or higher order) structures are not uncommon. Not always lattice based, though.
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
$endgroup$
A bornology is an example too.
A convexity structure is not a lattice (not closed under unions, just under
intersections and directed unions), but does have the "feel" of a topological structure, to me at least.
A convergence space is a set $X$ and a relation on the set of ultrafilters on it times $X$, etc. So such "second order" (or higher order) structures are not uncommon. Not always lattice based, though.
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
answered Mar 13 at 16:45
Henno BrandsmaHenno Brandsma
113k348123
113k348123
add a comment |
add a comment |
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– mrp
Mar 13 at 7:50
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Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here. For typesetting equations please use MathJax.
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– dantopa
Mar 14 at 3:01