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This wiki is for people who study hyperspaces, continuum theory, and, more generally, topology. Please create an account and contribute to the wiki. See our section on Problems such as a full transcription of The Houston Problem Book. Follow our Twitter.

Hyperspace theory

Containment hyperspace
Fell topology
Hit-and-miss topology
Hausdorff metric
Hyperspace
Hyperspace of closed subsets $\mathrm{CL}(X)$
Hyperspace of closed connected subsets $\mathrm{CLC}(X)$
Hyperspace of compact subsets $2^X$
Hyperspace of continua $C(X)$
$L$-convergence
Order arc
Sequential strong Whitney-reversible property
Strong Whitney-reversible property
Whitney map
Whitney property
Whitney-reversible property
Vietoris topology

General topology

Absolute retract
Aposyndetic
Arcwise connected
Cantor set Cantor set.png
Closure
Compact
Connected im kleinen
Cone
Compactum
Connected
Continuous
Disconnected
Delta connected
Function
Homeomorphism
Homogeneous
Homotopically unstable
Hurewicz
Limit inferior
Limit point
Limit superior
Lindelöf
Local separating point
Locally arcwise connected
Locally connected
Metric space
Metrizable
Monotone
Order of A in X
Peano space
Pelczyński compactum Pelczynski compactum.png
Separable
Strongly homotopically stable
Strongly Hurewicz
Superstable
Subbase
Topological space
Unstable
Zero-dimensional

Continuum theory

Absolute end point
Arc-like
Branch point
Chainable continuum
Composant
Confluent
Continuum
Decomposable
Epsilon map
Hausdorff Continuum
Hereditarily decomposable
Hereditarily indecomposable
Hereditarily unicoherent
Indecomposable
Inverse limit
Irreducible continuum
Kelley continuum
Knaster continuum
Menger-Urysohn order
Nondegenerate
Peano continuum
Property S
Rational
Rational continua
Real curve
Semicircle continuum
Sierpiński curve
Smoothness
Standard universal dendrite
Subcontinuum
Suslinean
Tree-like
Unicoherent

Examples of continua

Arc
Boxes continuum Boxes continuum.gif
Buckethandle Buckethandle.png
Cantor fan Cantorfan.png
Cantor organ Cantor organ.gif
Circle with a spiral Circlewithspiralfortheta=0totheta=40.png
Dendrite
Dendrite $P$ DendriteP.png
Dendroid
Dunce hat
$\lambda$-dendroid
Fan
Gehman dendrite Gehman dendrite.gif
Graph
Harmonic fan Harmonicfan.png
Harmonic shredded fan Harmonic shredded fan.gif
Hawaiian earring Hawaiianearring.png
Hairy point Hairy point.png
Hilbert cube
Hurewicz continuum
$\infty$-fin Infinity-fin.png
Lelek fan Lelek fan.gif
Lakes of Wada Lakes of Wada.jpg
Locally connected fan Locally connected fan.gif
Locally connected comb
M continuum M continuum.gif
Makuchowski umbrella Makuchowski umbrella.gif
$n$-cell
$n$-sphere
$n$-fin N-fin.png
$n$-od Simple n-od.png
Omiljanowski dendrite Omiljanowski dendrite.gif
Peano continuum
Pseudo-arc
Pseudo-circle
Pseudo-solenoid
Semicircle continuum Semicircle continuum.gif
Sierpiński carpet Sierpinskicarpet.png
Sierpiński triangle Sierpinski triangle.gif
Sin addiction continuum Sinaddictioncontinuum.png
Snake continuum Snake continuum.gif
Solenoid Smale-Williams Solenoid Large.png
Topologist's sine curve Topologistsinecurve.png
Trapezoid basins continuum Trapezoid basins continuum.gif
Tree
Triod
Warsaw circle Warsawcircle.png
Waraszkiewicz's spirals
Ważewski universal dendrite Wazewski.png
Zig-zag circle Zigzagcircle.png

External links

Encyclopedia of Compactness Wiki*
Examples in Continuum Theory
History of Continuum Theory
Open problems in continuum theory
University of Houston Mathematics Problem Book (10/14/94)
Pavel Pyrih Problem Book