TY - JOUR

T1 - The fundamental groups of one-dimensional spaces and spatial homomorphisms

AU - Eda, Katsuya

PY - 2002/9/30

Y1 - 2002/9/30

N2 - Let X be a one-dimensional metric space and ℍ be the Hawaiian earring.(1) Each homomorphism from π1(ℍ) to π1(X) is induced from a continuous map up to the base-point-change isomorphism on π1(X).(2) Let X be a one-dimensional Peano continuum. Then X has the same homotopy type as that of ℍ if and only if π1(X) is isomorphic to π1(ℍ), if and only if X has a unique point at which X is not semi-locally simply connected. (3) Let X and Y be one-dimensional Peano continua which are not semi-locally simply connected at any point. Then, X and Y are homeomorphic if and only if π1(X) and π1(Y) are isomorphic. Moreover, each isomorphism from π1(X) to π1(Y) is induced by a homeomorphism from X to Y up to the base-point-change-isomorphism.

AB - Let X be a one-dimensional metric space and ℍ be the Hawaiian earring.(1) Each homomorphism from π1(ℍ) to π1(X) is induced from a continuous map up to the base-point-change isomorphism on π1(X).(2) Let X be a one-dimensional Peano continuum. Then X has the same homotopy type as that of ℍ if and only if π1(X) is isomorphic to π1(ℍ), if and only if X has a unique point at which X is not semi-locally simply connected. (3) Let X and Y be one-dimensional Peano continua which are not semi-locally simply connected at any point. Then, X and Y are homeomorphic if and only if π1(X) and π1(Y) are isomorphic. Moreover, each isomorphism from π1(X) to π1(Y) is induced by a homeomorphism from X to Y up to the base-point-change-isomorphism.

KW - Fundamental group

KW - Hawaiian earring

KW - One-dimensional

KW - Spatial homomorphism

UR - http://www.scopus.com/inward/record.url?scp=0038690246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038690246&partnerID=8YFLogxK

U2 - 10.1016/S0166-8641(01)00214-0

DO - 10.1016/S0166-8641(01)00214-0

M3 - Article

AN - SCOPUS:0038690246

VL - 123

SP - 479

EP - 505

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 3

ER -