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In terms of the natural topology on the fundamental group, a locally path-connected space is semi-locally simply connected if and only if its quasitopological fundamental group is discrete.
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are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat
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in French). In particular, this condition is necessary for a space to have a simply connected covering space.
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The
Hawaiian earring can also be used to construct a semi-locally simply connected space that is not
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and therefore semi-locally simply connected, but it is clearly not locally simply connected.
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is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in
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A simple example of a space that is not semi-locally simply connected is the
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120:. The standard example of a non-semi-locally simply connected space is the
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Discreteness and homogeneity of the topological fundamental group
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35:Appears to be too technical for a non-expert.
31:needs attention from an expert in Mathematics
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405:Topologie algébrique: Chapitres 1 à 4
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407:. Springer. Ch. IV pp. 339 -480.
230:of U to the fundamental group of
473:Properties of topological spaces
253:Most of the main theorems about
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368:Topology of fundamental group
155:with the property that every
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68:semi-locally simply connected
195:must be contractible within
97:between covering spaces and
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421:J.S. Calcut, J.D. McCarthy
360:on the Hawaiian earring is
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108:Most “nice” spaces such as
33:. The specific problem is:
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171:(i.e. every loop in
167:to a single point within
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191:: though every loop in
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329:. Give this space the
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263:locally path-connected
78:. Roughly speaking, a
356:. In particular, the
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95:Galois correspondence
183:). The neighborhood
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463:Algebraic topology
435:Algebraic Topology
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401:Bourbaki, Nicolas
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226:from the
140:if every
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