Some results on \(\widetilde I(L)\) and \(\widetilde R(L)\) (Q1367500)

Let \((L^X,\delta)\) be a fuzzy topological space, and for \(A\in\delta\), \(a\in L\) (a lattice), \(A[a]= \{x\in X\mid A(x)\nleq a\}\). Consider the topology \(\delta^*\) on \(L^X\), \(\delta^*\) is generated by the subbase \(\delta\cup\{A[a]\mid A\in\delta\), \(a\in L\}\). We call \((L^X,\delta^*)\) a weak inducification of \((L^X,\delta)\) [\textit{D. Zhang} and the reviewer, Acta Math. Sin. 36, No. 1, 68-73 (1993; Zbl 0783.54009)]. In the paper under review, the author investigates the weak inducifications of the fuzzy unit interval \(i(L)\) and the fuzzy real \(R(L)\) [\textit{B. Hutton}, J. Math. Anal. Appl. 50, 74-79 (1975; Zbl 0297.54003)], denoted by \(\widetilde{I}(L)\) and \(\widetilde{R}(L)\), respectively. He gives a result on the connectedness of \(\widetilde{I}(L)\) and some properties of \(\widetilde{R}(L)\).