We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. show that implies and ⊤-uniform with countable bases, are equivalent. As an illustration of the applicability concept, we give a fixed point theorem certain contractive self-mappings in space. This result yields, as special case, probabilistic metric spaces.

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces is equivalent to sequential compactness. We also show Hausdorff compact are metrizable. the second part article discuss significance bottom sets fixed point theorems for mappings acting spaces.

The basic properties of the C-metric are well known. It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structur...

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric spaces. without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorem, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy metric spaces. We show that completeness of the whol...

In a recent paper [16] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of runcontinuous paths; we noted that there are different definitions of “length space” (also known as “path-metric space” or “intrinsic space”). In this paper we continue the analysis of asymmetric metric spaces. We propose possible definitions of completeness and (l...

An internal characterization of metric spaces which are absolute Borel sets of multiplicative classes is given. This characterization uses complete sequences of covers, a notion introduced by Froĺık for characterizing Čechcomplete spaces. We also show that the absolute Borel class of X is determined by the uniform structure of the space of continuous functions Cp(X); however the case of absolut...

<p>A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness the equivalent to property larger class includes continuous as well discontinuous mappings. In addition it, satisfying (ϵ - δ) non-expansive established.</p>

In the present paper we prove a fixed point theorem for one parameter family of contractive self-mappings, complete metric space or b-metric space, each member which has unique that is also common family; mappings may be continuous discontinuous at point. We under assumption weaker form continuity property satisfying conditions employed by us implies completeness underlying space. The character...

Today, great observatories around the world, devote a substantial amount of observing time to sky surveys. The resulted images are inputs of source finder modules. These modules search for the target objects and provide us with source catalogues. We sought to quantify the ability of detection tools in recovering faint galaxies regularly encountered in deep surveys. Our approach was based on com...