Applied General Topology - Vol 01, No 1 (2000)
https://riunet.upv.es:443/handle/10251/81885
Mon, 20 May 2024 18:12:33 GMT2024-05-20T18:12:33ZOn domains witnessing increase in information
https://riunet.upv.es:443/handle/10251/150095
On domains witnessing increase in information
Spreen, Dieter
[EN] The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well know, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and strongly regular Scott domains with continuous maps. Here a Scott domains is strongly regular if all of its compact open subsets are regular open. In one considers only embeddings of dependent products and sums. Moreover, they are w-cocomplete and their object classes are closed under several constructions used in programming language semantics. It follows that recursive domains equations can be solved and models of typed and untyped lambda calculi can be constructed. Both kinds of domains can be udes in giving meaning to programming language constructs.
Tue, 15 Sep 2020 11:38:12 GMThttps://riunet.upv.es:443/handle/10251/1500952020-09-15T11:38:12ZFuzzy functions: a fuzzy extension of the category SET and some related categories
https://riunet.upv.es:443/handle/10251/81900
Fuzzy functions: a fuzzy extension of the category SET and some related categories
Höhle, Ulrich; Porst, Hans-E.; Sostak, Alexander P.
[EN] In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.
Mon, 29 May 2017 09:43:57 GMThttps://riunet.upv.es:443/handle/10251/819002017-05-29T09:43:57ZPreservation of completeness under mappings in asymmetric topology
https://riunet.upv.es:443/handle/10251/81899
Preservation of completeness under mappings in asymmetric topology
Künzi, Hans-Peter A.
[EN] The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserved under uniformly open continuous surjections. Furthermore in the realm of quasi-uniform spaces conditions under which almost uniformly open mappings are uniformly open are given which generalize corresponding classical results for uniform spaces. As a by-product it is shown that a quasi-metrizable Moore space admits a left K-complete quasi-metric if and only if it is a complete Aronszajn space.
Mon, 29 May 2017 09:41:45 GMThttps://riunet.upv.es:443/handle/10251/818992017-05-29T09:41:45ZSeparation axioms in topological preordered spaces and the existence of continuous order-preserving functions
https://riunet.upv.es:443/handle/10251/81898
Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions
Bosi, Gianni; Isler, R.
[EN] We characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular.
Mon, 29 May 2017 09:39:10 GMThttps://riunet.upv.es:443/handle/10251/818982017-05-29T09:39:10ZJungck theorem for triangular maps and related results
https://riunet.upv.es:443/handle/10251/81896
Jungck theorem for triangular maps and related results
Grinc, M.; Snoha, L.
[EN] We prove that a continuous triangular map G of the n-dimensional cube In has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.
Mon, 29 May 2017 09:37:18 GMThttps://riunet.upv.es:443/handle/10251/818962017-05-29T09:37:18ZUseful topologies and separable systems
https://riunet.upv.es:443/handle/10251/81894
Useful topologies and separable systems
Herden, G.; Pallack, A.
[EN] Let X be an arbitrary set. A topology t on X is said to be useful if every continuous linear preorder on X is representable by a continuous real valued order preserving function. Continuous linear preorders on X are induced by certain families of open subsets of X that are called (linear) separable systems on X. Therefore, in a first step useful topologies on X will be characterized by means of (linear) separable systems on X. Then, in a second step particular topologies on X are studied that do not allow the construction of (linear) separable systems on X that correspond to non representable continuous linear preorders. In this way generalizations of the Eilenberg Debreu theorems which state that second countable or separable and connected topologies on X are useful and of the theorem of Estévez and Hervés which states that a metrizable topology on X is useful, if and only if it is second countable can be proved.
Mon, 29 May 2017 09:34:57 GMThttps://riunet.upv.es:443/handle/10251/818942017-05-29T09:34:57ZExtension properties and the Niemytzki plane
https://riunet.upv.es:443/handle/10251/81892
Extension properties and the Niemytzki plane
Ohta, Haruto
[EN] The first part of the paper is a brief survey on recent topics concerning the relationship between C*-embedding and C-embedding for closed subsets. The second part studies extension properties of the Niemytzki plane NO. A zero-set, z-; C*-, and P-embedded subsets of NP are determined. Finally, we prove that every C*-embedded subset of NP is a P-embedded zero-set, which answers a problem raised in the first part.
Mon, 29 May 2017 09:30:44 GMThttps://riunet.upv.es:443/handle/10251/818922017-05-29T09:30:44ZSome properties of o-bounded and strictly o-bounded groups
https://riunet.upv.es:443/handle/10251/81891
Some properties of o-bounded and strictly o-bounded groups
Hernández, C.; Robbie, D.; Tkachenko, Mikhail
[EN] We continue the study of (strictly) o-bounded topological groups initiated by the first listed author and solve two problems posed earlier. It is shown here that the product of a Comfort-like topological group by a (strictly) o-bounded group is (strictly) o-bounded. Some non-trivial examples of strictly o-bounded free topological groups are given. We also show that o-boundedness is not productive, and strict o-boundedness cannot be characterized by means of second countable continuous homomorphic images.
Mon, 29 May 2017 09:28:22 GMThttps://riunet.upv.es:443/handle/10251/818912017-05-29T09:28:22ZAn operation on topological spaces
https://riunet.upv.es:443/handle/10251/81889
An operation on topological spaces
Arhangelskii, A.V.
[EN] A (binary) product operation on a topological space X is considered. The only restrictions are that some element e of X is a left and a right identity with respect to this multiplication, and that certain natural continuity requirements are satisfied. The operation is called diagonalization (of X). Two problems are considered: 1. When a topological space X admits such an operation, that is, when X is diagonalizable? 2. What are necessary conditions for diagonalizablity of a space (at a given point)? A progress is made in the article on both questions. In particular, it is shown that certain deep results about the topological structure of compact topological groups can be extended to diagonalizable compact spaces. The notion of a Moscow space is instrumental in our study.
Mon, 29 May 2017 09:26:07 GMThttps://riunet.upv.es:443/handle/10251/818892017-05-29T09:26:07ZMerotopies associated with quasi-uniformities
https://riunet.upv.es:443/handle/10251/81888
Merotopies associated with quasi-uniformities
Császár, Ákos
[EN] To an arbitrary quasi-uniformity on the set X, a merotopy on X is assigned. There are results concerning the question whether this merotopy is compatible with the topology induced by the quasi-uniformity end whether the closure operation induced by the merotopy, admits a compatible uniformity. More precise results are obtained in the case of transitive quasi-uniformities.
Mon, 29 May 2017 09:23:28 GMThttps://riunet.upv.es:443/handle/10251/818882017-05-29T09:23:28Z