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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue

Vol 15 - Issue 4 (September 2024)

Advances in Pure and Applied Mathematics


List of Articles

Morphology of the connected components of the boolean sum of two digraphs (≤ 5)-hypomorphic up to complementation
Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour

Let $$$G=(V,E)$$$ and $$$G'=(V,E')$$$ be two digraphs, $$$(\leq 5)$$$-hypomorphic up to complementation, and $$$U:=G\dot{+} G'$$$ be the boolean sum of $$$G$$$ and $$$G'$$$. The case where $$$U$$$ and $$$\overline U$$$ are both connected was studied by the authors and B.Chaari giving the form of the pair$$$\{G, G'\}$$$. In this paper we study the case where $$$U$$$ is not connected and give the morphology of the pair $$$\{G_{\restriction {V({\mathcal C})}},G'_{\restriction {V({\mathcal C})}}\}$$$ whenever $$$C$$$ is a connected component of $$$U$$$.


Kan extendable subcategories and fibrewise topology
Moncef Ghazel

We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of general use. Here we apply them particularly to the study of the properties of certain categories of fibrewise topological spaces. In particular, we prove that the categories of fibrewise compactly generated spaces, fibrewise sequential spaces and fibrewise Alexandroff spaces are cartesian closed provided that the base space satisfies the right separation axiom.