In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

  In this paper, we define the bg**-connected space and study the relation between this space and other kinds of connected spaces .Also we study some types of continuous functions and study the relation among (connected space, b-connected space,  bg-connected  space and bg**-connected space) under these types of continuous functions.  

    The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.  

The chemical properties of chemical compounds and their molecular structures are intimately connected. Topological indices are numerical values associated with chemical molecular graphs that help in understanding the physicochemical properties, chemical reactivity and biological activity of a chemical compound. This study obtains some topological properties of second and third dominating David derived (DDD) networks and computes several K Banhatti polynomial of second and third type of DDD.

In this work the effect of annealing temperature on the structure and the electrical properties of Bi thin films was studied, the Bi films were deposited on glass substrates at room temperature by thermal evaporation technique with thickness (0.4 µm) and rate of deposition equal to 6.66Å/sec, all samples are annealed in a vacuum for one hour. The X-ray diffraction analysis shows that the prepared samples are polycrystalline and it exhibits hexagonal structure. The electrical properties of these films were studied with different annealing temperatures, the d.c conductivity for films decreases from 16.42 ? 10-2 at 343K to 10.11?10-2 (?.cm)-1 at 363K. The electrical activation energies Ea1 and Ea2 increase from 0.031 to 0.049eV and

Cadmium Oxide and Bi doped Cadmium Oxide thin films are prepared by using the chemical spray pyrolysis technique a glass substrate at a temperature of (400?C) with volumetric concentration (2,4)%. The thickness of all prepared films is about (400±20) nm. Transmittance and Absorbance spectra are recorded in the wave length ranged (400-800) nm. The nature of electronic transitions is determined, it is found out that these films have directly allowed transition with an optical energy gap of (2.37( eV for CdO and ) 2.59, 2.62) eV for (2% ,4%) Bi doped CdO respectively. The optical constants have been evaluated before and after doping.

Nano crystalline copper sulphide (Cu2S) thin films pure and 3% Bi doped were deposited on glass substrate by thermal evaporation technique of thickness 400±20 nm under a vacuum of ~ 2 × 10− 5 mbar to study the influence of annealing temperatures ( as-deposited, and 573) K on structural, surface morphology and optical properties of (Cu2S and Cu2S:3%Bi). (XRD) X-ray diffraction analysis showed (Cu2S and Cu2S:3%Bi) films before and after annealing are polycrystalline and hexagonal structure. AFM measurement approves that (Cu2S and Cu2S:3%Bi) films were Nano crystalline with grain size of (105.05-158.12) nm. The optical properties exhibits good optical absorption for Cu2S:3%Bi films. Decreased of optical band gap from 2.25 to 2 eV after dop

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.