background image

Funcoids and relations between filters

By definition

X

[

f

]

Y ⇔ Y ⊓ h

f

iX

0

F

(

B

)

.

We have

X

[

f

]

Y ⇔ Y ⊓ h

f

iX

0

F

(

B

)

⇔ X ⊓ h

f

iY

0

F

(

A

)

.

For brevity I will also define:

h

f

i

X

=

h

f

i↑

A

X

and

X

[

f

]

Y

⇔ ↑

A

X

[

f

]

B

Y .

A funcoid

f

is completely characterized by the relation

[

f

]

and even by

h

f

i

or

[

f

]

.

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