In the paper the “way-below” relation, in symbols x y, is introduced. Some authors prefer the term “relatively compact” or “way inside”, since in the poset of open sets of a topology it is natural to read U V as “U is relatively compact in V ”. A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a t...

We show a general method of construction of non-porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non-porous Suslin subset of a topologically complete metric space contains a non-porous closed subset. We show also a suucient condition, which gives that a certain system of compact sets contains a non-porous element. Namely, if we d...

For (b), let Θ be any subset of Γ, x in its complement, U as in (a). The neighbourhood xU of x contains at most one element of Γ. There exists a neighbourhood of x contained in xU and not containing any element of Θ. For (c), let V be the closure of U ·U, which is compact. The intersection of Γ with V is compact, and covered by disjoint neighbourhoods of each of its points. This intersection mu...

For (b), let Θ be any subset of Γ, x in its complement, U as in (a). The neighbourhood xU of x contains at most one element of Γ. There exists a neighbourhood of x contained in xU and not containing any element of Θ. For (c), let V = U ·U, which is compact. The intersection of Γ with V is compact, and covered by disjoint neighbourhoods of each of its points. This intersection must therefore be ...

It has been demonstrated that the ordinary boundary layer elements play an essential role in the finite element approximations for singularly perturbed problems producing ordinary boundary layers. Here we revise the element so that it has a small compact support and hence the resulting linear system becomes sparse, more precisely, block tridiagonal. We prove the validity of the revised element ...

In this paper we address the potential gain of using compact MIMO antenna array configurations in conjunction with High Altitude Platforms (HAPs) diversity techniques in order to increase the capacity in HAP communication systems. For this purpose, we also propose a novel compact MIMO antenna which we denote as the “MIMOOctahedron” and compare its performance with the vector element antenna. Si...

Printed sinusoidal monopoles are a type of meander line antennas, with smooth curve structure and enhanced performance, suitable for building compact multi-element antennas (MEAs). The antennas described here were designed at 2-3 GHz to meet the size and bandwidth constraints of multimedia sensor networks. Their performance was characterized in terms of electrical size, bandwidth, and broadband...

Proof of concept of a cavity backed slot antenna based on inverted microstrip gap ‎waveguide (IMGW) technology is presented. Since the antenna is operating based on the ‎first resonating mode of the cavity, it is more compact compared to the ordinary cavity ‎backed slot antennas in which the second cavity mode is used for radiation. Furthermore, ‎the proposed antenna element introduces lower lo...

In this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎We study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎