Dimension of the isometry group in three-dimensional Riemannian spaces

The Isometry Group of a Riemannian Manifold with boundary

The Isometry Dimension and Orbit Number of a Finite Group

A finite set W ⊂ R is said to realize the group G if the isometry group of W is isomorphic to G. The isometry dimension of a group is the minimum dimension of a realization. It is known that the isometry dimension of G is less than |G| [1]. We show that the isometry dimension of Z2 is n. The orbit number of a group is the minimum number of orbits in a realization. We show that the groups Z2 are...

Reflexivity of the Isometry Group of Some Classical Spaces

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. 4. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions. In...

a comparative study of the theme of "marriage" in three victorian novelists: charles dickens, george eliot and thomas hardy

این تحقیق کوشیده است با انتخاب پنج رمان از میان آثار برگزیده، «چارلز دیکنز»، «جورج الیوت» و «توماس هاردی » و با رویکردی تطبیقی به بررسی درونمایه ی «ازدواج» در آثار این سه رمان نویس بزرگ دوره ی ویکتوریا بپردازد. فرضیه ی اولیه ی تحقیق این بوده است که چارلز دیکنز (1870- 1812) با زبانی شوخ و گزنده، جورج الیوت(1880- 1819) با نگاهی آموزشی–اندرزگونه و توماس هاردی(1928- 1840) با رویکردی تلخ وانتقادی به...

Isometry of Polish metric spaces

We consider the equivalence relation of isometry of separable, complete metric spaces, and show that any equivalence relation induced by a Borel action of a Polish group on a Polish space is Borel reducible to this isometry relation. We also consider the isometry relation restricted to various classes of metric spaces, and produce lower bounds for the complexity in terms of the Borel reducibili...