In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only metric. It admits to remove constraints imposed usually on metric (the triangle axiom and nonnegativity of the squared metric), and to use the metric space ...

A metric on binary trees is dehed to give the similarity of two dendrograms. One of the major desirable properties of the proposed treesimilaritymeasure is to clarify the decision ordering nature of biological trees. This metric is applied to evolutionary tree reconstructions and comparative embryo-genesis. The mathematical properties of this metric are discussed, and an algofithm is proposed t...

This paper defines and discusses the Hausdorff metric on the space of nonempty, closed, and bounded subsets of a given metric space. We consider two important topological properties, completeness and total boundedness. We prove that each of these properties is posessed by a Hausdorff metric space if the property is possesed by the underlying metric space. Finally, we explore applications of the...

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We decribe a number of properties of a median metric space. In particular, we show that a complete connected median metric of finite rank admits a cononical bilipschitz equivalent CAT(0) metric. Metric spaces of this sort arise, up to bilipschitz equivalence, as asymptotic cones of certain classes of finitely generated groups, and the existence of such a structure has various consequences for t...

We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field (K, |·|) directly, but rather the associated projective spaces KP, as bounded metric structures. We show that the class of (projective spaces over) metric valued ...

The complexity (quasi-metric) space has been introduced as a part of the development of a topological foundation for the complexity analysis of algorithms ([12]). Applications of this theory to the complexity analysis of Divide & Conquer algorithms have been discussed in [12]. Here we obtain several quasi-metric properties of the complexity space. The main results obtained are the Smyth-complet...

We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays.