Results 1 - 10
of
119
Directed sets, nets, ideals, filters, and maps
- Journal of Formalized Mathematics
, 1996
"... Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8 ..."
Abstract
-
Cited by 109 (29 self)
- Add to MetaCart
(Show Context)
Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8, p. 2]), the definition of ideals and filters and the definition of maps preserving arbitrary and directed sups and arbitrary and filtered infs (1.9 also in [8, p. 4]). The concepts of semilattices, sup-semiletices and poset lattices (1.8 in [8, p. 4]) are also introduced. A number of facts concerning the above notion and including remarks 1.4, 1.5, and 1.10 from [8, pp. 3–5] is presented.
Boolean posets, posets under inclusion and products of relational structures
- Journal of Formalized Mathematics
, 1996
"... Summary. In the paper some notions useful in formalization of [11] are introduced, e.g. the definition of the poset of subsets of a set with inclusion as an ordering relation. Using the theory of many sorted sets authors formulate the definition of product of relational structures. ..."
Abstract
-
Cited by 84 (17 self)
- Add to MetaCart
(Show Context)
Summary. In the paper some notions useful in formalization of [11] are introduced, e.g. the definition of the poset of subsets of a set with inclusion as an ordering relation. Using the theory of many sorted sets authors formulate the definition of product of relational structures.
Galois Connections
, 1997
"... The paper is the Mizar encoding of the chapter 0 section 3 of [12] In the paper the following concept are defined: Galois connections, Heyting algebras, and Boolean algebras. ..."
Abstract
-
Cited by 52 (0 self)
- Add to MetaCart
The paper is the Mizar encoding of the chapter 0 section 3 of [12] In the paper the following concept are defined: Galois connections, Heyting algebras, and Boolean algebras.
Moore-Smith Convergence
, 2003
"... The paper introduces the concept of a net (a generalized sequence). The goal is to enable the continuation of the translation of [14]. ..."
Abstract
-
Cited by 32 (2 self)
- Add to MetaCart
The paper introduces the concept of a net (a generalized sequence). The goal is to enable the continuation of the translation of [14].
Cartesian Products of Relations and Relational Structures
, 1996
"... In this paper the definitions of cartesian products of relations and relational structures are introduced. Facts about these notions are proved. This work is the continuation of formalization of [8]. ..."
Abstract
-
Cited by 20 (6 self)
- Add to MetaCart
(Show Context)
In this paper the definitions of cartesian products of relations and relational structures are introduced. Facts about these notions are proved. This work is the continuation of formalization of [8].
The lattice of domains of an extremally disconnected space
- Formalized Mathematics
, 1992
"... ..."
(Show Context)
