TY - JOUR
T1 - A locally simply connected space and fundamental groups of one point unions of cones
AU - Eda, Katsuya
PY - 1992
Y1 - 1992
N2 - Let CX be the cone over a space X. Let a space X be first countable at x, then the following are equivalent: (1) X is locally simply connected at x; (2) Π1((X, x) ⩗ (X, x), x) is naturally isomorphic to the free product Π1(X, x)*Π1 (X, x); (3) Π1((CX, x)V(CX, x), x) is trivial. There exists a simply connected, locally simply connected Tychonoff space X with x ∈ X, such that (X, x) ⩗ (X, x) is not simply connected.
AB - Let CX be the cone over a space X. Let a space X be first countable at x, then the following are equivalent: (1) X is locally simply connected at x; (2) Π1((X, x) ⩗ (X, x), x) is naturally isomorphic to the free product Π1(X, x)*Π1 (X, x); (3) Π1((CX, x)V(CX, x), x) is trivial. There exists a simply connected, locally simply connected Tychonoff space X with x ∈ X, such that (X, x) ⩗ (X, x) is not simply connected.
KW - Cone
KW - First countable
KW - Fundamental group
KW - Locally simple
KW - One point union
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U2 - 10.1090/S0002-9939-1992-1132409-0
DO - 10.1090/S0002-9939-1992-1132409-0
M3 - Article
AN - SCOPUS:84966211913
VL - 116
SP - 239
EP - 249
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 1
ER -