Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces

In this paper, we contribute to infrasoft topology which is one of the recent generalizations of soft topology. Firstly, we redefine the concept of soft mappings to be convenient for studying the topological concepts and notions in different soft structures. Then, we introduce the concepts of open, closed, and homeomorphism mappings in the content of infrasoft topology. We establish main properties and investigate the transmission of these concepts between infrasoft topology and its parametric infratopologies. Finally, we define a quotient infrasoft topology and infrasoft quotient mappings and study their main properties with the aid of illustrative examples.

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.

Some new results on six types mappings between L-convex spaces

The aim of this paper is devoted to present some new results on six types of special mappings between L-convex spaces. For this purpose, we first make a summary about some novel elementary properties of L-CP mappings and L-CC mappings. Secondly, we propose the definitions of almost LCC mappings, L-isomorphic mappings and L-embedding mappings and investigate their fundamental characterizations. Finally, we establish the connections between L-quotient mappings and L-quotient spaces. As a summary, we give a diagram to show the relationships among all the above-mentioned mappings.