Editing Counterexamples in Topology (section)

==List of mentioned counterexamples==
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#[[finite set|Finite]] [[discrete topology]]
#[[Countable]] [[discrete topology]]
#Uncountable [[discrete topology]]
#[[Indiscrete topology]]
#[[Partition topology]]
#[[Odd–even topology]]
#[[Deleted integer topology]]
#[[Particular point topology|Finite particular point topology]]
#[[Particular point topology|Countable particular point topology]]
#[[Particular point topology|Uncountable particular point topology]]
#[[Sierpiński space]], see also [[particular point topology]]
#[[Closed extension topology]]
#Finite [[excluded point topology]]
#Countable [[excluded point topology]]
#Uncountable [[excluded point topology]]
#[[Open extension topology]]
#[[Either-or topology]]
#[[Finite complement topology]] on a [[countable]] space
#[[Finite complement topology]] on an uncountable space
#[[Countable complement topology]]
#Double pointed [[countable complement topology]]
#[[Compact complement topology]]
#Countable [[Fort space]]
#Uncountable [[Fort space]]
#[[Fortissimo space]]
#[[Arens–Fort space]]
#Modified [[Fort space]]
#[[Euclidean space|Euclidean topology]]
#[[Cantor set]]
#[[Rational number]]s
#[[Irrational number]]s
#Special subsets of the real line
#Special subsets of the plane
#[[One point compactification]] topology
#One point compactification of the rationals
#[[Hilbert space]]
#[[Fréchet space]]
#[[Hilbert cube]]
#[[Order topology]]
#Open ordinal space [0,Γ) where Γ<Ω
#Closed ordinal space [0,Γ] where Γ<Ω
#Open ordinal space [0,Ω)
#Closed ordinal space [0,Ω]
#Uncountable discrete ordinal space
#[[Long line (topology)|Long line]]
#[[Long line (topology)|Extended long line]]
#An altered [[Long line (topology)|long line]]
#[[Lexicographic order topology on the unit square]]
#[[Order topology|Right order topology]]
#[[Order topology|Right order topology on '''R''']]
#[[Lower limit topology|Right half-open interval topology]]
#[[Nested interval topology]]
#[[Overlapping interval topology]]
#[[Interlocking interval topology]]
#Hjalmar Ekdal topology, whose name was introduced in this book.
#[[Prime ideal topology]]
#[[Divisor topology]]
#[[Evenly spaced integer topology]]
#The [[P-adic#Analytic approach|''p''-adic topology]] on '''Z'''
#Relatively [[prime integer topology]]
#[[Prime integer topology]]
#Double pointed reals
#Countable complement extension topology
#[[K-topology|Smirnov's deleted sequence topology]]
#[[Rational sequence topology]]
#Indiscrete rational extension of '''R'''
#Indiscrete irrational extension of '''R'''
#Pointed rational extension of '''R'''
#Pointed irrational extension of '''R'''
#Discrete rational extension of '''R'''
#Discrete irrational extension of '''R'''
#Rational extension in the plane
#[[Telophase topology]]
#[[Double origin topology]]
# [[Irrational slope topology]]
#Deleted diameter topology
#Deleted radius topology
#[[Half-disk topology]]
#Irregular lattice topology
#[[Arens square]]
#Simplified [[Arens square]]
#[[Moore plane|Niemytzki's tangent disk topology]]
#Metrizable tangent disk topology
#[[Sorgenfrey plane|Sorgenfrey's half-open square topology]]
#Michael's product topology
#[[Tychonoff plank]]
#[[Deleted Tychonoff plank]]
#[[Alexandroff plank]]
#[[Dieudonné plank]]
#Tychonoff corkscrew
#Deleted Tychonoff corkscrew
#[[Hewitt's condensed corkscrew]]
#[[Thomas's plank]]
#[[Thomas's corkscrew]]
#[[Split interval|Weak parallel line topology]]
#Strong parallel line topology
#Concentric circles
#[[Appert space]]
#Maximal compact topology
#Minimal [[Hausdorff topology]]
#[[Alexandroff square]]
#'''Z<sup>Z</sup>'''
#Uncountable products of '''Z'''<sup>+</sup>
#Baire product metric on '''R'''<sup>ω</sup>
#'''I<sup>I</sup>'''
#[0,Ω)×'''I<sup>I</sup>'''
#[[Helly space]]
#'''C'''[0,1]
#[[Box topology|Box product topology]] on '''R'''<sup>ω</sup>
#[[Stone–Čech compactification]]
#[[Stone–Čech compactification]] of the integers
#[[Novak space]]
#Strong ultrafilter topology
#Single ultrafilter topology
#Nested rectangles
#[[Topologist's sine curve]]
#[[Topologist's sine curve|Closed topologist's sine curve]]
#[[Topologist's sine curve|Extended topologist's sine curve]]
#[[Infinite broom]]
#[[Closed infinite broom]]
#[[Integer broom]]
#Nested angles
#Infinite cage
#[[Bernstein's connected sets]]
#[[Gustin's sequence space]]
#[[Roy's lattice space]]
#[[Roy's lattice subspace]]
#[[Knaster-Kuratowski fan|Cantor's leaky tent]]
#[[Cantor's teepee]]
#[[Pseudo-arc]]
#[[Miller's biconnected set]]
#Wheel without its hub
#[[Tangora's connected space]]
#Bounded metrics
#[[Sierpinski's metric space]]
#[[Duncan's space]]
#[[Cauchy completion]]
#[[Hausdorff distance|Hausdorff's metric]] topology
#[[Post Office metric]]
#Radial metric
#Radial interval topology
#[[Bing's discrete extension space]]
#[[Michael's closed subspace]]
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