Contents

• PRELIMINARIES
• LOCALLY CONNECTED CONTINUA
  • Basic examples: an arc, a circle, -cube , Hilbert cube
  • Graphs
  • Dendrites
    • Preliminary properties
    • Simple examples
    • The locally connected fan
    • The locally connected combs
    • Universal dendrites
    • Wazewski universal dendrite
    • Universal dendrites of order
    • Other universal dendrites
    • The dendrite
    • Self-homeomorphic dendrites
    • Monotone equivalence and monotone homogeneity
    • Omiljanowski dendrite
    • Chaotic and rigid dendrites
    • Miller dendrite
    • Dendrites of de Groot-Wille type
    • Modified Miller dendrites
    • Dendrites with the closed set of end points
    • Gehman dendrite
    • Modifications of the Gehman dendrite
    • Mapping hierarchy of dendrites
  • Cyclic examples of locally connected continua
    • Menger universal continua
    • Sierpinski carpet
    • Menger universal curve
  • 2-dimensional locally connected continua
  • Higher dimensional locally connected continua
  • Variations of local connectedness
  
  
• JOINING PROPERTIES
  • Cut points and separating points (also local)
  • Arcwise connectedness; arc components
  • Continuum chainability
  • Various kinds of connectedness (-connectedness, -connectedness, etc.)
  
  
• DECOMPOSABLE AND INDECOMPOSABLE CONTINUA
  • Decomposable continua (also hereditary)
  • Indecomposable continua (also hereditary)
    • Knaster continua
  • Unicoherent continua (also hereditary)
  • Discoherent continua
  • Multicoherent continua
  
  
• IRREDUCIBLE CONTINUA
  • Elementary examples
    • Sin curve
    • Cantor organ and accordion
  • Arc-like (chainable) continua
  • Irreducible circle-like continua
    • Solenoids
  • Compactifications of the real line and the real half-line
  • Other examples
  
  
• USC DECOMPOSITIONS OF CONTINUA
  • Decomposition spaces
  • Upper semi-continuous decompositions
  • Continuous decompositions
  
  
• CURVES
  • Order of a space at a point
  • Case-Chamberlin examples
  • Curves without arcs
  • Covering defined classes (inverse limit expansions)
  • Other examples
  
  
• FAMILIES OF CONTNINUA
  • Universal elements
  • Common models
  • Families of incomparable continua
  
  
• PLANE CONTINUA
  • Embeddability of continua in surfaces
  • Planability in general
  • Planability of graphs on of locally connected continua
  • Separation of the plane
  
  
• MAPPINGS
  • Various kinds of mappings and relations between them
  
  
• CONTINUA WITH SPECIAL MAPPING PROPERTIES
  • Existence of special mappings
  • Self-similar continua
  • Self-homeomorphic continua
  • Rigid continua
  • Chaotic continua
  • Absolute retracts; spaces and
  • Absolute retracts for various classes of continua
  • Class (W) and other classes defined by mappings
  • Homogeneity
  • Variations of homogeneity
  • Generalized homogeneity
  • Embeddability in
  • Weakly chainable continua
  • Fixed point property
  
  
• CONTINUA AS FRACTALS
• DYNAMICAL SYSTEMS
  • Attractors
  
  
• OTHER PROPERTIES
  • Colocal connectedness
  • Aposyndesis and its variations
  • Property of Kelley (also hereditary)
  • Smoothness
  • Arc-smoothness
  • -smoothness
  
  
• NEW FIGURES
  • New examples 1
    • Whyburn's curve
    • Pseudo-arc
    • Zig-zag circle
    • M-continuum
    • Cantor interaction
    • Pseudo-circle
    • Semicircle continuum
    • Boxes continuum
  • New examples 2
    • Graph
    • Graph
    • Space filling curve
    • Universal arc-like continuum
    • Lakes of Vada
    • Borsuk fan
    • Ingram's atriodic continuum
    • Double Warsaw circle
    • Warsaw circle
    • Crooked Warsaw circle
  • New examples 3
    • Young spiral
    • Young space
    • Bing space
    • Universal smooth dendroid
    • Claytor's curve A
    • Claytor's curve B
    • Sin addiction continuum
    • Dumbbell
    • Figure Eight
    • Noose
  • New examples 4
    • Theta curve
    • Trapezoid basins continuum
    • Dragon continuum
  • New examples 5
    • Harmonic fan
    • Harmonic shredded fan
    • Cantor fan
    • Lelek fan
  • New examples 6
    • Sierpinski triangle
    • Makuchowski umbrella
    • Snake
    • Cantor snake
    • Cruller
  • New examples 7
    • Cantor comb
    • Gehman dendrite on ski
    • Makuchowski twin
    • Cantor function comb
    • Oversteegen's dendroid
  
  
• Definitions
  • absolute end point
  • absolute retract
  • absolutely terminal continuum
  • acyclic
  • almost chainable
  • aposyndetic
  • arc
  • arc-smooth
  • arc-structure
  • atomic
  • atriodic
  • biconnected
  • bihomogeneous
  • Borel sets
  • branch point
  • chainable
  • chaotic
  • circle
  • completely regular
  • composant
  • confluent
  • -connected
  • connected im kleinen
  • continuous selection of
  • converges homeomorphically to the continuum
  • converge 0-regularly
  • convex
  • continuum
  • contractible
  • curve
  • cut point
  • -smooth
  • cyclic element
  • decomposable
  • deformation retract of
  • dendroid
  • dendrite
  • dispersion point
  • end point
  • equivalent
  • -equivalent
  • feebly monotone
  • finitely Suslinean
  • finitely linear
  • fixed point
  • fixed set property
  • fixed point self-homeomorphic
  • fixed ball self-homeomorphic
  • free arc
  • graph
  • half-ray curve
  • hereditary
  • hereditarily
  • hereditarily decomposable
  • hereditarily equivalent
  • hereditarily indecomposable
  • hereditarily locally connected
  • hereditarily unicoherent
  • homogeneous
  • HU-terminal
  • hyperspace
  • indecomposable
  • induced mapping
  • inverse limit
  • irreducible
  • light
  • like
  • locally
  • locally confluent
  • local homeomorphism
  • local separating point
  • MO-mapping
  • monotone map
  • mutually aposyndetic
  • natural projection
  • neat
  • near homeomorphism
  • OM-mapping
  • open map
  • openly minimal
  • orbit
  • order
  • order preserving mapping
  • ordinary point
  • periodic point of
  • periodic-recurrent property
  • pointwise self-homeomorphic
  • pseudo-arc
  • pseudo-confluent
  • property of Kelley
  • quasi-monotone
  • radially convex at
  • ramification point
  • rational
  • real curve
  • recurrent point of
  • refinable (monotonely)
  • regular
  • retract, retraction
  • rigid
  • selectible
  • scattered
  • self-homeomorphic
  • semi-aposyndetic
  • semi-confluent
  • semi-continuum
  • semi-continuous
  • semi-locally connected
  • simple closed curve
  • simple -od
  • simple triod
  • shore point
  • smooth (dendroid)
  • strongly chaotic
  • strongly pointwise self-homeomorphic
  • strongly rigid
  • strongly self-homeomorphic
  • strongly unicoherent1
  • strongly unicoherent2
  • Suslinean
  • terminal continuum
  • thin
  • translation
  • tree
  • triod
  • unicoherent
  • uniformly continuum-chainable
  • uniquely arcwise connected
  • universal
  • weak cut point
  • weakly chainable
  • weakly confluent
  • weakly hereditarily unicoherent
  • weakly monotone
  • weakly smooth at a point
  • weakly Suslinian
  • widely connected
  • width
  
  
• List of examples
• Technical information
• Index
• Bibliography
• About this document ...