On the \(L\)-fuzzy Brouwer fixed point theorem
Let \(L\) be a fuzzy lattice, i.e. a completely distributive lattice with an order-reversing involution. In the paper, the authors prove successfully that (1) the \(L\)-cube has the fixed point property (under the Hutton product \(L\)-topology); (2) the stratified \(L\)-cube is formed by the product of \(I^*(L)\) which is the stratification of the \(L\)-fuzzy interval \(I(L)\) [\textit{B. Hutton}, J. Math. Anal. Appl. 50, 74-79 (1975; Zbl 0297.54003)]. The stratified \(L\)-cubes have also the fixed point property when \(L\) has a countable base. The result (1) is a generalization of one obtained by \textit{T. Kubiak} [ibid. 223, No. 1, 62-66 (1998; Zbl 0907.54006)], under a rather strong assumption.
scientific article; zbMATH DE number 1339627
scientific article