Unicoherent Space
المؤلف:
Charatonik, J. J. and Prajs, J. R.
المصدر:
"On Local Connectedness of Absolute Retracts." Pacific J. Math. 201
الجزء والصفحة:
...
30-7-2021
1784
Unicoherent Space
Let 
be a connected topological space. Then 
is unicoherent provided that for any closed connected subsets 
and 
of 
, if 
, then 
is connected.
An interval, say [0,1], is unicoherent, but a circle, say ![S^1=<span style=]()
{e^(itheta):theta in [0,2pi]} subset= C" src="https://mathworld.wolfram.com/images/equations/UnicoherentSpace/Inline8.gif" style="height:21px; width:154px" />, is not unicoherent. An interesting example of a unicoherent space is a ray winding down on a circle. Specifically, let 
, where ![W=<span style=]()
{(1+1/(1+theta))e^(itheta):0<=theta<infty} subset= C" src="https://mathworld.wolfram.com/images/equations/UnicoherentSpace/Inline10.gif" style="height:23px; width:198px" />. Then the space 
, illustrated above, is unicoherent.
REFERENCES:
Charatonik, J. J. and Prajs, J. R. "On Local Connectedness of Absolute Retracts." Pacific J. Math. 201, 83-88, 2001.
Mackowiak, T. "Retracts of Hereditarily Unicoherent Continua." Bull. Acad. Polon. Sci. Ser. Sci. Math. 28, 177-183, 1980.
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