The notions of closedness and D-connectedness in quantale-valued approach spaces

Document Type: Research Paper


1 Department of Mathematics, School of Natural Sciences, National University of Sciences & Technology, Islamabad.

2 Department of Mathematics, Faculty of Art & Science, Hacı Bektaş Veli University, Nevşehir, Turkey


In this paper, we characterize local $T_{0}$ and $T_{1}$ quantale-valued gauge spaces, show how these concepts are related to each other and apply them to $\mathcal{L}$-approach distance spaces and $\mathcal{L}$-approach system spaces. Furthermore, we give the characterization of a closed point and $D$-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each other.


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