In this paper, we show that a regular space with a locally countable weak-base is g-metrizable. Secondly, we establish the relationships between spaces with a locally countable weak-base (resp. spaces with a locally countable weak-base consisting of א0-subspaces) and metric spaces (resp. locally separable metric spaces) by means of compact-covering maps, 1-sequence-covering maps, compact maps, ...

The goal of this paper is to explore basic topics in Algebraic Topology. The paper will first begin by exploring the concept of loops on topological spaces and how one can look at these loops and form a group. From there, it moves to discuss covering spaces giving basic definitions and constructing the universal cover. After establishing this, covering spaces are used to calculate the fundament...

The model of the torus as a parallelogram in the plane with opposite sides identiied enables us to deene two families of parallel lines and to tessellate the torus, then to associate to each tessellation a toroidal map with an upward drawing. It is proved that a toroidal map has a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embe...

Background and Objective: The most common intravascular brachytherapy sources include 32P, 188Re, 106Rh and 90Sr/90Y. In this research, skin absorbed dose for different covering materials in dealing with these sources were evaluated and the best covering material for skin protection and reduction of absorbed dose by radiation staff was recognized and recommended.Method: Four materials including...