‎For the subclasses $\mathcal{M}_1$ and $\mathcal{M}_2$ of‎‎monomorphisms in a concrete category $\mathcal{C}$‎, ‎if $\mathcal‎{M}_2\subseteq \mathcal{M}_1$‎, ‎then $\mathcal{M}_1$-injectivity‎‎implies $\mathcal{M}_2$-injectivity& More
‎For the subclasses $\mathcal{M}_1$ and $\mathcal{M}_2$ of‎‎monomorphisms in a concrete category $\mathcal{C}$‎, ‎if $\mathcal‎{M}_2\subseteq \mathcal{M}_1$‎, ‎then $\mathcal{M}_1$-injectivity‎‎implies $\mathcal{M}_2$-injectivity‎. ‎The Baer type criterion is about‎ ‎the converse of this fact‎. ‎In this paper‎, ‎we apply injectivity to the classes of $C$-dense‎, ‎$C$-closed‎ ‎monomorphisms‎. ‎The concept of quasi injectivity is also introduced here to‎ ‎investigte the Baer type criterion for these notions‎.
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In this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. We introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some More
In this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. We introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.
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