On I-quotient mappings and I-cs'-networks under a maximal ideal

<p>Let I be an ideal on N and f : X → Y be a mapping. f is said to be an I-quotient mapping provided f−1(U) is I-open in X, then U is I-open in Y . P is called an I-cs′-network of X if whenever {xn}n∈N is a sequence I-converging to a point x ∈ U with U open in X, then there is P ∈ P and some n0 ∈ N such that {x, xn0} ⊆ P ⊆ U. In this paper, we introduce the concepts of I-quotient mappings and I-cs′-networks, and study some characterizations of I-quotient mappings and I-cs′- networks, especially J -quotient mappings and J -cs′-networks under a maximal ideal J of N. With those concepts, we obtain that if X is an J -FU space with a point-countable J -cs′-network, then X is a meta-Lindelöf space.</p>

A New Class on Ng# α-Quotient Mappings in Nano Topological Space

The primary intend of this article is to define a new class of mappings called Ng# α-quotient mappings in nano topological space. The intention is to analyze characterizations and inter relationship of Ng# α-quotient mappings with nano Tg#α-space, Ng# α-continuous, Ng# α-open, Ng# α-irresolute, Ng# α-homeomorphism and nano α-quotient mapping. Also several properties of strongly Ng# α-quotient mapping are derived and the relationships among them are illustrated with the help of examples. Their interesting composition with strongly Ng# α-irresolute are established. The concept of Ng# α-quotient mapping is explored and composition of mappings under strongly Ng# α-quotient mapping and Ng# α-quotient mapping are discussed. Furthermore, to emphasize Ng# α-quotient mapping a few examples are considered and derived in detail.

Do large Polish cities substitute their own-source revenues with fees and user charges?

This paper aims to assess if large Polish cities use fees and user charges to substitute other own-source revenues. The analysis has been conducted on a panel of 65 large cities in Poland in the period of 2004-2015. Using OLS and fixed effect panel analysis, it has been proved that cities pursue their policy in order to maximize their revenues, which is in line with the Leviathan theory assuming that public authorities maximize public revenues. Additionally, using the normalization quotient mapping, it has been confirmed that cities do not change their revenue policy in terms of taxes vs. fees and user charges trade-offs.

Quotient structure of interior-closure texture spaces

In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T0 reflection. Finally, we introduce some classes of quotient difunctions such as bi-initial and bi-final difunctions between interior-closure texture spaces.

Some properties of C-reflexive locally convex spaces

In this note, we shall prove that the class of C-reflexive spaces is stable with respect to separated quotient, arbitrary product and sum, which is not the case for the closed subspaces and the dense hyper planes. If the quotient mapping lifts compact disks, then the class of C-reflexive spaces is three-space stable.

Essentially Convexoid Operators

Let H be a separable complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. Let π be the quotient mapping from B(H) onto the Calkin algebra B(H)/K(H), where K(H) denotes all compact operators on B(H). An operator T ∈ B(H) is said to be convexoid[14] if the closure of its numerical range W(T) coincides with the convex hull co σ(T) of its spectrum σ(T). T ∈ B(H) is said to be essentially normal, essentially G1, or essentially convexoid if π(T) is normal, G1 or convexoid in B(H)/K(H) respectively.