A note on nearness spreads in frames (Q536497)

A spread on frames is a frame homomorphism \(h:M\rightarrow L\) between locally connected frames for which \(x\in L\) is a component of \(h(y)\) for some \(y\in M\). In this short article the author deals with nearness spreads, that is, spreads \((M,h,L)\) between locally connected regular frames where \(M\) carries the fine nearness Cov\((M)\) (consisting of all covers of \(M\)) and \(L\) carries the corresponding induced nearness \(\mathfrak{N}^h L\) (generated by the covers \(C_A=\{x\in L\mid x\) is a component of \(h(a)\) for some \(a\in A\}\), \(A\in \text{Cov}(M)\)).