arXiv subjects

Anika Njamcul

Publications and source records attributed to Anika Njamcul.

3 recordsLinked to original sources

arXiv2023

On topology expansion using ideals

Topologies can be expanded with the help of ideals, using the local function, an operator resembling the closure of a set. The aim of this paper is to define the ideals which enable us to create this topology $τ^{*}$ on $X$ simultaneously making a specific set $A\subseteq X$ open in $τ^{*}$. We study certain properties of $τ^{*}$, especially under the assumption that $A$ is a preopen set. Further, we reflect on the ideal topological space in which the ideal is generated by a chosen family of dense sets. Here we prove that the generated topology by this ideal is submaximal, but not maximal connected.

math.GN↗

arXiv2022

Various types of continuity and their interpretations in ideal topological spaces

This paper is a continuation of work started in \cite{njampavcont} on preserving continuity in ideal topological spaces. We will deal with $θ$-continuity and weak continuity and give their translations in ideal topological spaces. As consequences of those results, we will prove that every $θ$-continuous function is continuous if topologies are generated by $θ$-open sets and we will give an example of weakly continuous function which is not $τ_θ$-continuous. This will complete the diagram of relations between continuous, $τ_θ$-continuous, $θ$-continuous, weakly continuous and faintly continuous functions.

math.GN↗

arXiv2021

On preserving continuity in ideal topological spaces

We present some sufficient conditions for continuity of the mapping $f:\langle X,τ_X^*\rangle \to \langle Y,τ_Y^*\rangle$, where $τ_X^*$ and $τ_Y^*$ are topologies induced by the local function on $X$ and $Y$, resp. under the assumption that the mapping from $\langle X, τ_X \rangle$ to $\langle Y, τ_Y \rangle$ is continuous. Further, we consider open and closed functions in this matter, as we state the cases in which the open (or closed) mapping is being preserved through the "idealisation" of both domain and codomain. Through several examples we illustrate that the conditions we considered can not be weakened.

math.GN↗