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On some gross misunderstandings about the theory of topological molecular lattices. (English) Zbl 0941.54005

After introducing the theory of topological molecular lattices (TML) [G.-J. Wang, ibid. 30, No. 1, 53-62 (1989; Zbl 0667.54001); 47, No. 3, 351-376 (1992; Zbl 0783.54032)] some authors established the equivalence between the category of TML and the known category, for example, a category consisting of a certain kind of bitopological spaces (see the review by M. Erné of [G.-J. Wang, ibid. 47, loc. cit.] in M.R. 93h:06008), and another example, a category [T.-H. Fan, Acta Math. Sin. 35, No. 5, 598-605 (1992; Zbl 0768.54003)]. The authors of the paper under review claim that (1) the translation derived from the category equivalence can be sometimes quite difficult. (2) The TMS is a new subject with many peculiar features. The discussion is interesting.

MSC:

54A40 Fuzzy topology
06D10 Complete distributivity
06B30 Topological lattices
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