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Index

adjoint

lower, 24
upper, 24

α

-totally bounded, 225

α

-thick, 224

antitone, 24
antitone order embedding, 24
antitone order isomorphism, 24
associative

infinite, 54

atom, 22
atomic, 22
atomistic, 23

ball

closed, 127
open, 127

β

-thick, 224

β

-totally bounded, 225

bounded above, 16
bounded below, 16
bounds

lower, 17
upper, 17

category, 31

abrupt, 328
dagger, 43
of funcoid triples, 151
of funcoids, 151
of pointfree funcoid triples, 293
of pointfree funcoids, 293
of reloid triples, 182
of reloids, 182
partially ordered, 43
quasi-invertible, 310
with star-morphisms, 327

induced by dagger category, 329
quasi-invertible, 328

category theory, 31
chain, 16
closed

regarding pointfree funcoid, 300

closure

in metric space, 128
Kuratowski, 132

co-completion

funcoid

pointfree, 297

of funcoid, 166
of reloid, 186

complement, 20
complemented

element, 20
lattice, 20

complementive, 20
complete

multifuncoid, 360
staroid, 360

complete lattice

homomorphism, 24

completely starrish, 79
completion

of funcoid, 166
of reloid, 186

composable

funcoids, 139
reloids, 176

composition

funcoids, 139
of reloids, 176

concatenation, 50
connected

regarding endofuncoid, 220
regarding endoreloid, 220
regarding pointfree funcoid, 300

connected component, 219
connectedness

regarding binary relation, 218
regarding

Rel

-endomorphism, 218

connectivity reloid, 219
continuity

coordinate-wise, 353
generalized, 213
of restricted morphism, 215
pre-topology, 212
proximity, 212
uniformity, 212

converges

regarding funcoid, 268

core part, 87

dual, 87

core star, 89
currying, 48, 49

De Morgan’s laws

infinite, 21

decomposition of composition, 207

388