The symmetric group S , is a metric space with distance d(a , b ) = IE(a-'b)( where E ( c ) is the set of points moved by c E S,. Let L be a given subset of {I. 2, . . . , n}, a permutation clique A = A(L, n ) is any subset A c S , with d(a, b ) E L whenever a, b E A , a # b. We give a framework of new and known information o n some special A = A ( L , n): maximal, largest, largest subgroups of...

in this manuscript, we prove some coupled fixed point theoremsfor two pairs of self mappings satisfying contractive conditions of integraltype in generalized metric spaces. we furnish suitable illustrative examples.in this manuscript, we prove some coupled fixed point theoremsfor two pairs of self mappings satisfying contractive conditions of integraltype in generalized metric spaces. we furnis...

Low-energy dynamics in the unit-charge sector of the CP 1 model on spherical space (space-time S × R) is treated in the approximation of geodesic motion on the moduli space of static solutions, a sixdimensional manifold with non-trivial topology and metric. The structure of the induced metric is restricted by consideration of the isometry group inherited from global symmetries of the full field...

A metric of non-negative sectional curvature on the direct product S2 × S2 of two two-spheres may be introduced as follows: take spheres (S2 i , gi), i = 1, 2 with rotationally symmetric metrics of non-negative curvature and consider the factor space of (S2, g1) × (S2, g2) × S1 by the action of the family of isometries Ĩτ (φ1, φ2) acting as the composition of a rotation of the first factor by a...

Kripke’s schema with parameters turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke’s schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructi...

Less roughly: Two figures in a space1 S are are isometric iff there is a distance-preserving bijection between the points of one and the points of the other. It is common to talk as if we can ‘move’ a geometric figure around in a given space. That’s loose. Better to think of it like this: some regions of a given space are translations, rotations, or reflections of other regions of the space. Th...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

Low-energy dynamics in the unit-charge sector of the CP 1 model on spherical space (space-time S 2 × R) is treated in the approximation of geodesic motion on the moduli space of static solutions, a six-dimensional manifold with non-trivial topology and metric. The structure of the induced metric is restricted by consideration of the isometry group inherited from global symmetries of the full fi...