Index Index
\(\delta\)-neighborhood of a point in a metric space, Section
\(T_1\)-space, Definition
\(T_2\)-space, Definition
\(T_3\)-space, Definition
\(T_4\)-space, Definition
accumulation point in a metric space, Definition
Archimedean property, Theorem
basic open set, Paragraph
basis
elements, Paragraph
for a topology, Definition
boundary in a topological space, Definition
boundary point in a metric space, Definition
boundary point in a topological space, Definition
bounded subset of \(\R^n\), Definition
box topology, Definition
cardinality of a set, Paragraph
Cartesian product, Definition
Cauchy sequence, Activity
Cauchy-Schwarz Inequality, Lemma
clopen set in a topological space, Section
closed set in a topological space, Definition
closed subset of a metric space, Definition
closure in topological spaces, Definition
closure of a set in a metric space, Definition
compact subset, Definition
component, Definition
composition of functions, Definition
connected space, Definition Item
continuity at a point in a metric space, Definition
continuity in a topological space, Definition
continuous function, Definition
convergent sequence in a topological space, Definition
coordinate space, Paragraph
cover, Definition
open, Definition
cut point, Definition
cut set, Definition
derived set, Paragraph
digital arc, Definition
digital Jordan curve, Definition
digital line topology, Exercise
digital path, Definition
equivalence relation, Definition
factor space, Paragraph
finite set, Definition
Frechet space, Definition
function, Definition
bijection, Definition
codomain, Item
domain, Item
identity, Paragraph
injection, Definition
inverse, Definition
open, Definition
range, Item
restriction, Definition
surjection, Definition
Hausdoff space, Definition
hereditary property, Definition
Hilbert space, Exercise
homeomorphic spaces, Paragraph
homeomorphism, Definition
identification space, Paragraph
identity function, Activity
image of an element, Item
indexed family of sets, Activity
induced topology, Section
infimum, Paragraph
interior of a set, Definition
interior point, Definition
interior point in a subset of a metric space, Definition
interval, Definition
isolated point, Definition
isolated point in a metric space, Definition
isometry, Definition
Klein bottle, Paragraph
least upper bound, Paragraph
limit of a sequence in a metric space, Definition
limit of a sequence in a topological space, Paragraph
limit of a sequence of real numbers, Definition
limit point in a metric space, Definition
limit point in a topological space, Definition
locally compact, Definition
locally connected, Definition
lower bound, Definition
metric, Definition
discrete, Paragraph
Euclidean, Paragraph
Hamming, Definition
Hausdorff, Definition
Levenshtein, Definition
max, Paragraph
taxicab, Preview Activity
metric space, Definition
complete, Activity
metrically equivalent, Definition
metrizable topological space, Paragraph
minimal neighborhood, Definition
Möbius strip, Activity
neighborhood in a metric space, Definition
neighborhood in a topological space, Definition
normal topological space, Definition
open ball in a metric space, Definition Definition
open function, Definition
open set in a metric space, Definition
open sets in a topological space, Paragraph
path, Definition
path component, Definition
path connected, Definition
locally, Definition
path product, Definition
power set, Exercise
preimage of an element, Item
product metric, Paragraph
product metric space, Definition
product topology, Definition Paragraph
projection functions, Paragraph
real projective plane, Exercise
regular topological space, Item
relation, Definition
relative topology, Section
relatively closed set, Activity
relatively open set, Section
retract, Exercise
retraction, Exercise
separation, Definition
sequence in a metric space, Definition
sequence in a topological space, Definition
set, Paragraph
arbitrary intersection, Activity
arbitrary union, Activity
complement, Item
intersection, Item
union, Item
set difference, Item
Sorgenfrey line, Exercise
subbase, Definition
subbasis, Definition
subspace of a metric space, Definition
subspace of a topological space, Definition
subspace topology, Section
supremum, Paragraph
topological invariant, Definition
topological property, Definition
topological space, Paragraph
topologically equivalent, Definition
topologist’s sine curve, Section
topology, Definition
cofinite, Activity
discrete, Item
Double Origin, Exercise
excluded point, Exercise
finite complement, Activity
indiscrete, Item
Khalimsky, Activity
lower limit, Exercise
particular point, Exercise
Zariski, Exercise
topology generated by a basis, Definition
triangle inequality, Paragraph
Zariski topology, Exercise
