Castellini, Gabriele Some remarks on interior operators and the functional property. (English) Zbl 1420.18001 Quaest. Math. 39, No. 2, 275-287 (2016). Summary: In this paper, functoriality of the notion of categorical interior operator is discussed and as a related topic, the property of \(\mathcal{F}\)-modal interior operator is introduced. Cited in 4 Documents MSC: 18A05 Definitions and generalizations in theory of categories 18B30 Categories of topological spaces and continuous mappings (MSC2010) 54B30 Categorical methods in general topology Keywords:interior operator; functorial property; open morphism; hereditary interior operator; modal interior operator PDFBibTeX XMLCite \textit{G. Castellini}, Quaest. Math. 39, No. 2, 275--287 (2016; Zbl 1420.18001) Full Text: DOI References: [1] Adámek, J.; Herrlich, H.; Strecker, G. E., Abstract and Concrete Categories (1990), Wiley: Wiley, New York · Zbl 0695.18001 [2] Castellini, G., Categorical Closure Operators, Mathematics: Theory and Applications (2003), Birkhäuser: Birkhäuser, Boston · Zbl 1045.18001 [3] Castellini, G., Interior operators in a category: idempotency and heredity, Topology Appl., 158, 2332-2339 (2011) · Zbl 1230.18002 · doi:10.1016/j.topol.2011.06.030 [4] Castellini, G., Interior operators, open morphisms and the preservation property, Appl. Categ. Structures, 23, 3, 311-322 (2015) · Zbl 1316.18002 · doi:10.1007/s10485-013-9337-4 [5] Castellini, G.; Murcia, E., Interior operators and topological separation, Topology Appl., 160, 1476-1485 (2013) · Zbl 1284.54024 · doi:10.1016/j.topol.2013.05.023 [6] Castellini, G.; Ramos, J., Interior operators and topological connectedness, Quaest. Math., 33, 3, 290-304 (2010) · Zbl 1274.54067 · doi:10.2989/16073606.2010.507322 [7] Dikranjan, D.; Giuli, E., Closure operators I, Topology Appl., 27, 129-143 (1987) · Zbl 0634.54008 · doi:10.1016/0166-8641(87)90100-3 [8] Dikranjan, D.; Tholen, W., Categorical Structure of Closure Operators, with Applications to Topology, Algebra and Discrete Mathematics (1995), Kluwer Academic Publishers: Kluwer Academic Publishers, Dordrecht · Zbl 0853.18002 [9] Holgate, D.; Slapal, J., Categorical neighborhood operators, Topology Appl., 158, 2356-2365 (2011) · Zbl 1232.54018 · doi:10.1016/j.topol.2011.06.031 [10] Razafindrakoto, A.; Holgate, D., Interior and neighborhood, Topology Appl., 168, 144-152 (2014) · Zbl 1321.18005 · doi:10.1016/j.topol.2014.02.019 [11] Vorster, S. J.R., Interior operators in general categories, Quaest. Math., 23, 405-416 (2000) · Zbl 0974.18003 · doi:10.2989/16073600009485987 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.