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funcoids
Entourages of a composition of funcoids ★★
Author(s): Porton
Conjecture
for every composable funcoids
and
.
![$ \forall H \in \operatorname{up} (g \circ f) \exists F \in \operatorname{up} f, G \in \operatorname{up} g : H \sqsupseteq G \circ F $](/files/tex/145d32f0a6448ea3d98f9b091370160956ba4532.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ g $](/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png)
Keywords: composition of funcoids; funcoids
Restricting a reloid to lattice Gamma before converting it into a funcoid ★★
Author(s): Porton
Conjecture
for every reloid
.
![$ (\mathsf{FCD}) f = \bigcap^{\mathsf{FCD}} (\Gamma (A ; B) \cap \operatorname{GR} f) $](/files/tex/d9afe4920809a29a644f5bc594e40f3313a8d527.png)
![$ f \in \mathsf{RLD} (A ; B) $](/files/tex/90326a901389c8760f7fa928fff117636a958338.png)
Keywords: funcoid corresponding to reloid; funcoids; reloids
Inner reloid through the lattice Gamma ★★
Author(s): Porton
Conjecture
for every funcoid
.
![$ (\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $](/files/tex/9c5b448dbc0964ca844d30e92247626e8d5420b5.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
Counter-example: for the funcoid
is proved in this online article.
Keywords: filters; funcoids; inner reloid; reloids
Coatoms of the lattice of funcoids ★
Author(s): Porton
Problem Let
and
be infinite sets. Characterize the set of all coatoms of the lattice
of funcoids from
to
. Particularly, is this set empty? Is
a coatomic lattice? coatomistic lattice?
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ B $](/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png)
![$ \mathsf{FCD}(A;B) $](/files/tex/d051d7da40c4a6b1d4234c0f74689d1bc7c994f1.png)
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ B $](/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png)
![$ \mathsf{FCD}(A;B) $](/files/tex/d051d7da40c4a6b1d4234c0f74689d1bc7c994f1.png)
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