Abstract
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.
Original language | English |
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Pages (from-to) | 239-249 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 116 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1992 |
Externally published | Yes |
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Keywords
- Cone
- First countable
- Fundamental group
- Locally simple
- One point union
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
A locally simply connected space and fundamental groups of one point unions of cones. / Eda, Katsuya.
In: Proceedings of the American Mathematical Society, Vol. 116, No. 1, 1992, p. 239-249.Research output: Contribution to journal › Article
}
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
UR - http://www.scopus.com/inward/record.url?scp=84966211913&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84966211913&partnerID=8YFLogxK
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 -