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## Contents

# 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

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

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

Buckethandle

Cantor fan

Cantor organ

Circle with a spiral

Dendrite

Dendrite $P$

Dendroid

Dunce hat

$\lambda$-dendroid

Fan

Gehman dendrite

Graph

Harmonic fan

Harmonic shredded fan

Hawaiian earring

Hairy point

Hilbert cube

Hurewicz continuum

$\infty$-fin

Lelek fan

Lakes of Wada

Locally connected fan

Locally connected comb

M continuum

Makuchowski umbrella

$n$-cell

$n$-sphere

$n$-fin

$n$-od

Omiljanowski dendrite

Peano continuum

Pseudo-arc

Pseudo-circle

Pseudo-solenoid

Semicircle continuum

Sierpiński carpet

Sierpiński triangle

Sin addiction continuum

Snake continuum

Solenoid

Topologist's sine curve

Trapezoid basins continuum

Tree

Triod

Warsaw circle

Waraszkiewicz's spirals

Ważewski universal dendrite

Zig-zag circle

# 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