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 , is not unicoherent.
An interesting example of a unicoherent space is a ray winding down on a circle.
Specifically, let ,
where .
Then the space ,
illustrated above, is unicoherent.
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.
be a connected topological space. Then 
is unicoherent provided that for any
closed connected subsets 
and 
of 
, if 
, then 
is connected.
![S^1={e^(itheta):theta in [0,2pi]} subset= C](/images/equations/UnicoherentSpace/Inline8.svg)
, is not unicoherent.
An interesting example of a unicoherent space is a ray winding down on a circle.
Specifically, let 
,
where 
.
Then the space 
,
illustrated above, is unicoherent.
