Abstract
We introduce a new concept of connectedness with respect to a categorical closure operator. The concept, which is based on using pseudocomplements in subobject semilattices, naturally generalizes the classical connectedness of topological spaces and we show that it also behaves accordingly. Moreover, as the main result, we prove that the connectedness introduced is preserved, under some natural conditions, by inverse images of subobjects under quotient morphisms. An application of this result in digital topology is discussed too.
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The author acknowledges support from the Ministry of Education of the Czech Republic, project no. MSM0021630518.
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Šlapal, J. Another Approach to Connectedness with Respect to a Closure Operator. Appl Categor Struct 17, 603–612 (2009). https://doi.org/10.1007/s10485-008-9163-2
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DOI: https://doi.org/10.1007/s10485-008-9163-2