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The
(topologist's)
sin curve
is defined by
 is irreducible between points and
,
. It has exactly three
end points and two arc components.
 It is one of the simplest arclike continua.
 It is a compactification of a ray
with remainder an arc.
 It has the periodicrecurrent
property [Charatonik et al. 1997b, Corollary 5.10, p. 117].
 The only possible confluent nondegenerate
images of are an arc and a continuum homeomorphic to
[Nadler 1977a].
 The hyperspace of all subcontinua of
is homeomorphic to the cone over
[Nadler 1977b].
See Figure A.
Figure 4.1.1:
( A ) sin curve

There are many variations of the sin curve. Some of them are pictured below.
See Figure BC.
Figure 4.1.1:
( B ) union of two sin curves

Figure 4.1.1:
( C ) union of two sin curves

Here you can find source files
of this example.
Here you can check the table
of properties of individual continua.
Here you can read Notes
or
write to Notes
ies of individual continua.
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Up: Elementary examples
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Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
20011130