\documentstyle{amsppt}

\nologo

\magnification 1200

\pageheight{17cm}

\pagewidth{30pc}

\vcorrection{0cm}



\define \Lim{\roman{Lim}\,}

\define \Li{\roman{Li}\,}

\define \Ls{\roman{Ls}\,}

\define \inter{\roman{int}\,}

\define \cl{\roman{cl}\,}

\define \bd{\roman{bd}\,}

\define \diam{\roman{diam}\,}

\define \ord{\roman{ord}\,}

\define \card{\roman{card}\,}

\define \nbh{neighborhood }

\define \nbhs{neighborhoods }

\define \nbhsk{neighborhoods. }

\define \cm{continuum }

\define \cmk{continuum. }

\define \cs{continuous }

\define \csk{continuous. }

\define \hyp{hyper\-space }

\define \hypk{hyper\-space. }

\define \eps{\varepsilon}



\document

\centerline{\bf{PROPERTIES OF CONTINUA}}

\bigskip

\par I. CONNECTIVITY PROPERTIES \medskip \noindent

1) Local connectedness (also hereditary) \newline

2) Connectedness im kleinen (also hereditary) \newline

3) Semi-local connectedness \newline

4) Number of nondegenerate arc components \newline

5) Arcwise connectedness (also hereditary) \newline

6) Continuum chainability (also hereditary ???) \newline

7) Aposyndeticity \newline

8) Variations of aposyndeticity

\bigskip

\par II. DECOMPOSABILITY PROPERTIES \medskip \noindent

1) Decomposability (also hereditary) \newline

2) Indecomposability (also hereditary) \newline

3) Unicoherence (also hereditary) \newline

4) Discoherence \newline

5) Degree of multicoherence \newline

6) Atriodicity

\bigskip

\par III. STRUCTURAL PROPERTIES \medskip \noindent

1) Graphs \newline

2) Rational continua \newline

3) Regular continua \newline

4) Suslinian continua \newline

5) Irreducible continua (also hereditary) \newline

6) Properties of (irreducible) continua related to decompositions and

decomposability of layers \newline

7) Dimension

\bigskip

\par IV. COVERING PROPERTIES \medskip \noindent

1) arc-like continua, chainable continua \newline

2) weakly chainable continua \newline

3) tree-like continua \newline

4) circle-like continua \newline

5) $\Cal P$-like continua

\bigskip

\par V. MAPPING PROPERTIES \medskip \noindent

1) Existence of special mappings \par

a) Retractions from hyperspaces \par

b) Means \par

c) Contractibility (also hereditary) \par

d) Selectibility \newline

2) Self-similar continua \newline

3) Self-homeomorphic continua \newline

4) Rigid continua \newline

5) Chaotic continua \newline

6) Absolute retracts \newline

7) Absolute retracts for various classes of continua \newline

8) Class (W) and other classes defined by mappings \newline

9) Homogeneity \newline

10) Variations of homogeneity \newline

11) Generalized homogeneity \newline

12) Embeddability in $\Bbb R^n$ \newline

13) Fixed point property

\bigskip

\par VI. OTHER PROPERTIES \medskip \noindent

1) Property of Kelley (also hereditary) \newline

2) Smoothness \newline

3) Arc-smoothness \newline

4) $C^*$-smoothness

\bigskip

\enddocument




