Intrinsic metric preserving maps on partially ordered groups |
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Authors: | M Jasem |
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Institution: | (1) Department of Mathematics Faculty of Chemistry, Slovak Technical University, SK-812 37 Bratislava, Slovakia |
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Abstract: | In 11] Pap proved that a surjective mapf from an abelian lattice ordered groupG
1 onto an abelian Archimedean lattice ordered group G2 which preserves non-zero intrinsic metricsd
1, andd
2 onG
1 andG
2, respectively (i.e.d
1(x,y)=d1(z, t) implies d2(f(x)f(y))= d2(f(z),f(t))) and satisfiesf(0)=0 is a homomorphism and put the question whether that assertion is true in the case that G2 is a non-Archimedean lattice ordered group. In this paper it is proved that a surjective map from an abelian directedG
1 onto a directed group G2 such thatf(0)=0 is a homomorphism if ¦x –y ¦=¦z – t¦ implies ¦f(x) –f(y)¦=¦f(z) –f(t)¦ and it is shown that the answer to the question of Pap is positive.Presented by M. Henriksen. |
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Keywords: | |
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