caa a22 4500 465779131 CHVBK 20180323111950.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF00401557 doi (NATIONALLICENCE)springer-10.1007/BF00401557 Sendlewski Andrzej Institute of Mathematics, Nicholas Copernicus University, Toruń, Poland aut Nelson algebras through Heyting ones: I [Elektronische Daten] [Andrzej Sendlewski] The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley ([15], [16]) for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described (Thm 2.3). The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction ([6], [25]) is also given (Thm 3.6). These results are applied to compare the equational category N of Nelson algebras and some its subcategories (and their duals) with the equational category H of Heyting algebras (and its dual). It is proved (Thm 4.1) that the category N is topological over the category H. Kluwer Academic Publishers, 1990 Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 105-126 0039-3215 49:1<105 1990 49 11225 https://doi.org/10.1007/BF00401557 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00401557 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sendlewski Andrzej Institute of Mathematics, Nicholas Copernicus University, Toruń, Poland aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 105-126 0039-3215 49:1<105 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer