Codenseness and openness with respect to an interior operator

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dc.contributor.authorAssfaw, F.S
dc.contributor.authorHolgate, D
dc.date.accessioned2021-04-15T11:34:22Z
dc.date.available2021-04-15T11:34:22Z
dc.date.issued2021
dc.description.abstractWorking in an arbitrary category endowed with a fixed (E, M) -factorization system such that M is a fixed class of monomorphisms, we first define and study a concept of codense morphisms with respect to a given categorical interior operator i. Some basic properties of these morphisms are discussed. In particular, it is shown that i-codenseness is preserved under both images and dual images under morphisms in M and E, respectively. We then introduce and investigate a notion of quasi-open morphisms with respect to i. Notably, we obtain a characterization of quasi i-open morphisms in terms of i-codense subobjects. Furthermore, we prove that these morphisms are a generalization of the i-open morphisms that are introduced by Castellini. We show that every morphism which is both i-codense and quasi i-open is actually i-open. Examples in topology and algebra are also provided.en_US
dc.identifier.citationAssfaw, F.S., & Holgate, D. (2021). Codenseness and openness with respect to an interior operator. Applied Categorical Structures ,29(2), 235-248en_US
dc.identifier.issn0927-2852
dc.identifier.uri10.1007/s10485-020-09614-w
dc.identifier.urihttp://hdl.handle.net/10566/6051
dc.language.isoenen_US
dc.publisherSpringer Natureen_US
dc.subjectCodensenessen_US
dc.subjectInterior operatoren_US
dc.subjectOpennessen_US
dc.subjectQuasi-opennessen_US
dc.titleCodenseness and openness with respect to an interior operatoren_US
dc.typeArticleen_US

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