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INDEX

300

destination, 26
difference, 16
directly isomorphic, 178
disjunction property of Wallman, 29
distance, 89
domain

of funcoid, 108

downgrading, 241

staroid, 241

dual

order, 12
poset, 12

duality

partial order, 12

E

edge, 26
edge part, 57
element

of filtrator, 49

embedding

reloids into funcoids, 159

endo-funcoid, 165
endomorphism, 27
endomorphism series, 165
endo-reloid, 165
equivalent

filters, 175

F

filter

closed, 131
cofinite, 81
Fréchet, 81
on a meet-semilattice, 49
on a poset, 49
on a set, 48
on meet-semilattice, 61
on poset, 61
on powerset, 76
on set, 76
principal, 49, 62
proper, 48
rebase, 175

filter base, 61

generalized, 67

of a filter, 67

generated by, 54

filter-closed, 55
filtrator, 49

central, 49
complete lattice, 49
down-aligned, 51
filtered, 50
lattice, 49
of funcoids, 104
powerset, 76
prefiltered, 50
semifiltered, 50
star-separable, 53
up-aligned, 51
with co-separable core, 51
with finitely join-closed core, 50

with finitely meet-closed core, 50
with join-closed core, 49
with meet-closed core, 50
with separable core, 51

finitary

relation

anchored, 239

finite intersection property, 81
form

of star-morphism, 254

free star

complete, 284

funcoid, 97, 98

co-complete, 120
complete, 120
destination, 98
identity, 108
induced by reloid, 146
injective, 129
monovalued, 129
open, 128
pointfree, 199

co-complete, 220
co-completion, 222
complete, 219
composable, 201
composition, 201
destination, 199
domain, 208
identity, 207
image, 207
injective, 223
monovalued, 223
order, 205
restricted identity, 207
restricting, 207
source, 199
zero, 271

principal, 103
restricted identity, 108
reverse, 98
source, 98

funcoidal reloid, 155
funcoids

composable, 99
composition, 99
separable, 131

function space of posets, 233

G

Galois

connection, 20

Galois connection

between funcoids and reloids, 153

generalized closure, 120

pointfree, 220

graph

of anchored relation, 40, 238

greatest element, 12, 13
Grothendieck universe, 10
group, 27

permutation, 27

transitive, 27