In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...

We discuss 1-Ahlfors-regular connected sets in a general metric space and prove that such sets are ‘flat’ on most scales and in most locations. Our result is quantitative, and when combined with work of I. Hahlomaa, gives a characterization of 1-Ahlfors regular subsets of 1Ahlfors-regular curves in metric spaces. Our result is a generalization to the metric space setting of the Analyst’s (Geome...

In this paper, some new fixed point theorems in Menger probabilistic metric spaces are established. And then, some common fixed point theorems are obtained. Applications to the fixed point theory in partially ordered Menger probabilistic metric spaces are given. Mathematics Subject Classification: 47H10, 54H25

The energy constrained wireless sensor nodes need very efficient localization algorithm for event detection. We propose a method for localizing the wireless sensor nodes using the concept of Cayley-Menger Determinants, which in turn uses a quadratic solver. This is a modification of the method proposed in Ref. [5]. Cayley-Menger Detereminants are used to introduce corrections to the noisy measu...

In this work, we introduce the notion of Menger probabilistic metric type space, on the other hand, we introduce a more general class of auxiliary functions in contractivity condition, following that, we obtain some multipled common fixed point theorems for a pair of mappings T : X×X · · · ×X } {{ } m-times → X and A : X→ X. As an application, we give out an example to demonstrate the validity ...

It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner’s proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdős space in the h...

For a compact Lie group G, we characterize free G-spaces that admit free Gcompactifications. For such G-spaces, a universal compact free G-space of given weight and given dimension is constructed. It is shown that if G is finite, the ndimensional Menger free G-compactum μn is universal for all separable, metrizable free G-spaces of dimension less than or equal to n. Some of these results are ex...

We discuss 1-Ahlfors-regular connected sets in a metric space. We prove that such a set is ‘flat’ on most scales and locations. We give a quantitative version of this. This, together with work of I. Hahlomaa, gives a characterization of 1-Ahlfors regular subsets of 1-Ahlfors-regular curves in a metric space, generalizing in a way the Analyst’s (Geometric) Traveling Salesman theorems by P. Jones...

In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for metric spaces [B. Singh, S. Jain, A fixed point ...