Measurability in the category of structural topological spaces

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Kurdistan, P. O. Box 416, 66177-15175 Sanandaj, Kurdistan, Iran.

10.48308/cgasa.2025.240590.1557

Abstract

In this paper, we first show that the category of measurable spaces is isomorphic to a particular category of structural topological spaces. Next, we define structural measurable space and we introduce a notion of structural outer measure  adapted to a topological structure, along with a corresponding concept of structural measure for objects in the category of structural topological spaces. These concepts are formulated in terms of functions, transformations and natural transformations. Next, we illustrate these concepts with various examples, including several fuzzy topological spaces. Finally, under certain conditions we prove a generalization of Carathéodory's Extension  and Carathéodory's Criterion showing that each notion -structural outer measure and structural measure- induces the other.  

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 28 April 2026

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