Simply Connected
المؤلف:
Croft, H. T.; Falconer, K. J.; and Guy, R. K.
المصدر:
Unsolved Problems in Geometry. New York: Springer-Verlag
الجزء والصفحة:
...
28-7-2021
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Simply Connected
A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the domain is connected but not simply, it is said to be multiply connected. In particular, a bounded subset 
of 
is said to be simply connected if both 
and 
, where 
denotes a set difference, are connected.
A space 
is simply connected if it is pathwise-connected and if every map from the 1-sphere to 
extends continuously to a map from the 2-disk. In other words, every loop in the space is contractible.
REFERENCES:
Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 2, 1991.
Krantz, S. G. Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 27, 1999.
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