We study the topological centers of some specific adjoints of a Banach module action. Then, we investigate the Arens regularity and strong irregularity of these actions.

quasi module is a new algebraic structure, based on module, which is composed of a semigroup structure and a partial order accompanied with an external ring multiplication. We proposed this structure in our paper [1] while we were studying the hyperspace C(M) consisting of all nonempty compact subsets of a topological module M over some topological ring R. quasi module can be considered as a generalisation of module in some sense. In the present paper we have defi ned topological quasi module and given some examples of it. We have shown that the Cartesian product of arbitrary family of topological quasi modules is again a topological quasi module over some topological unitary ring. Finally we have defi ned projective system of topological quasi modules and projective limit of this system. We have proved various topological properties of the projective limit of a projective system.

In this paper, the relations between separation axioms and (quasi)topological MV-algebras are studied. It is proved that T0-spaces and (T1) Hausdorff spaces are equivalent in (quasi) topological MV-algebras. Also, some topologies on MV-algebras are generated by ideals, filters and prefilters. It is shown that the MV-algebras equipped with these topologies are (para)topological MV-algebras and (T0) normal spaces. In addition, some conditions are derived for locally compact Hausdorff MV-algebras to make them into normal paratopological MV-algebras. Finally, quotient MV-algebras are studied to get a Hausdorff topological quotient MV-algebra.

For a normed space X, let JX : X ® X** denote the canonical embedding of X into X**, with the second adjoint (JX ) **: X**® X****. We defined MX (in Section 3 of the paper [1]) by MX = {x**Î 2 X** : JX**(x**) = (JX )**(x**)}….

Let X be a Baire space, Y be a W-space and Z be a regular topological space. We will show that every KC-function f: X´Y®Z is strongly quasi-continuous at each point of X´Y. In particular, when X is a Baire space and Y is Corson compact, every KC-function f from X´Y to a Moore space Z is jointly continuous on a dense subset of X´Y. We also give a few applications of our results on continuity of group actions.

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism ¦ between quasi irresolute topological groups is irresolute at eG, then ¦ is irresolute on G. Later we prove that in a semi-connected quasi irresolute topological group (G; *; Ƭ), if V is any symmetric semi-open neighborhood of eG, then G is generated by V. Moreover it is proven that a subgroup H of a quasi-irresolute topological group (G; *; Ƭ) is semi-discrete if and only if it has a semi-isolated point.

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In this paper, we obtain a new class of $(n+1)$-dimensional magnetic brane solutions of quasi-topological gravity in the presence of exponential and logarithmic nonlinear electrodynamics by a spinning magnetic branes with one or more rotation parameters. For the spinning brane, the brane has a net electric charge, when one or more rotation are non zero, and also this electric charge is proportional to the magnitude of the rotation parameter. However, when all the rotation parameters are zero (static brane), the electric field vanishes and the brane has no net electric charge. In the class of solutions, we have a spacetime with an angular magnetic field. These solutions are horizonless and have no curvature, but there is a conic singularity with a deficit angle. In addition, these two forms of nonlinear electrodynamics theory, have the same behaviors for the obtained solutions. Finally, we use the counterterm method and compute conserved quantities of these spacetimes.