Metric spaces with unique pretangent spaces. Conditions of the uniqueness
Annales Academiae Scientiarum Fennicae Mathematica, cilt.36, sa.1, ss.353-392, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 36 Sayı: 1
- Basım Tarihi: 2011
- Doi Numarası: 10.5186/aasfm.2011.3623
- Dergi Adı: Annales Academiae Scientiarum Fennicae Mathematica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.353-392
- Anahtar Kelimeler: Cantor set, Logarithmic spiral, Metric spaces, Pretangent spaces, Uniqueness of pretangent metric spaces
- Uşak Üniversitesi Adresli: Hayır
Özet
We find necessary and sufficient conditions for an arbitrary metric space X to have a unique pretangent space at a marked point a ∈ X. Applying this general result we show that each logarithmic spiral has a unique pretangent space at the asymptotic point. Unbounded multiplicative subgroups of C* = C\{0} having unique pretangent spaces at zero are characterized as lying either on the positive real semiaxis or on logarithmic spirals. Our general uniqueness conditions in the case X ⊆ R make it also possible to characterize the points of the ternary Cantor set having unique pretangent spaces.