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Index

A

adjoint

lower, 20
upper, 20

α

-thick, 171

α

-totally bounded, 172

associative

infinite, 46

atom, 19
atomic, 19
atomistic, 19

B

ball

closed, 89
open, 89

β

-thick, 171

β

-totally bounded, 172

bounds

lower, 14
upper, 14

C

category, 26

abrupt, 254
dagger, 36
of funcoid triples, 111
of funcoids, 110
of pointfree funcoid triples, 209
of pointfree funcoids, 209
of reloid triples, 140
of reloids, 140
partially ordered, 36
quasi-invertible, 231
with star-morphisms, 254

induced by dagger category, 255
quasi-invertible, 254

category theory, 26
chain, 13
closed

regarding pointfree funcoid, 224

closure

in metric space, 90
Kuratowski, 94

co-completion

funcoid

pointfree, 222

of funcoid, 125
of reloid, 143

complement, 17
complemented

element, 17
lattice, 17

complementive, 16
complete

multifuncoid, 287
staroid, 287

complete lattice

homomorphism, 20

completely starrish, 285
completion

of funcoid, 125
of reloid, 143

composable

funcoids, 99
reloids, 133

composition

funcoids, 99
of reloids, 133

concatenation, 41
connected

regarding endofuncoid, 168
regarding endoreloid, 168
regarding pointfree funcoid, 225

connected component, 167
connectedness

regarding binary relation, 166

connectivity reloid, 167
continuity

coordinate-wise, 276
generalized, 162
in metric space, 90
of restricted morphism, 163
pre-topology, 161
proximity, 161
uniformity, 161

converges

regarding funcoid, 226

core part, 50

dual, 50

core star, 52
currying, 40

D

De Morgan’s laws

infinite, 18

decomposition of composition, 157

of reloids, 157

299