Applied General Topology - Vol 09, No 2 (2008)

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https://riunet.upv.es/handle/10251/86405

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Semigroups and their topologies arising from Green's left quasiorder
Spread of balleans
On pseudo-k-spaces
A note on a fixed point theorem for ray oriented maps
Asymptotic proximities
Unitary representability of free abelian topological groups
On the topology of generalized quotients
Applications of pre-open sets
Probability measure monad on the category of ultrametric spaces
Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions
The Jordan curve theorem in the Khalimsky plane
On the continuity of factorizations
Scott-representability of some spaces of Tall and Miskin
On σ-starcompact spaces
On some variations of multifunction continuity
Review of the book of Vladimir Kovalevsky "Geometry of Locally Finite Spaces"

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Now showing 1 - 5 of 16

Review of the book of Vladimir Kovalevsky "Geometry of Locally Finite Spaces"
(Universitat Politècnica de València, 2008-10-01) Matveev, Sergei
No abstract.
On some variations of multifunction continuity
(Universitat Politècnica de València, 2008-10-01) Kanibir, A.; Reilly, Ivan L.
[EN] This paper considers six classes of multifunctions between topological spaces, namely almost ℓ−continuous multifunctions, K-almost c−continuous multifunctions, nearly continuous multifunctions, almost nearly continuous multifunctions, super continuous multifunctions, and δ−continuous multifunctions. We relate these classes of multifunctions to others, and provide characterizations of related concepts especially in terms of appropriate changes of topology.
On σ-starcompact spaces
(Universitat Politècnica de València, 2008-10-01) Song, Yan-Kui; National Science Foundation, China
[EN] A space X is σ-starcompact if for every open cover U of X, there exists a σ-compact subset C of X such that St(C, U) = X. We investigate the relations between σ-starcompact spaces and other related spaces, and also study topological properties of σ-starcompact spaces.
Scott-representability of some spaces of Tall and Miskin
(Universitat Politècnica de València, 2008-10-01) Bennet, Harold; Lutzer, David
[EN] In this paper we show that a variation of a technique of Miskin and Tall yields a cocompact completely regular Moore space that is Scott-domain-representable and has a closed Gδ-subspace that is not Scott-domain-representable. This clarifies the general topology of Scott-domain-representable spaces and raises additional questions about Scott-domain representability in Moore spaces.
On the continuity of factorizations
(Universitat Politècnica de València, 2008-10-01) Comfort, W.W.; Gotchev, Ivan S.; Recoder-Nuñez, Luis
[EN] Let {Xi : i ∈ I} be a set of sets, XJ :=Пi∈J Xi when Ø ≠ J ⊆ I; Y be a subset of XI , Z be a set, and f : Y → Z. Then f is said to depend on J if p, q ∈ Y , pJ = qJ ⇒ f(p) = f(q); in this case, fJ : πJ [Y ] → Z is well-defined by the rule f = fJ ◦ πJ|Y When the Xi and Z are spaces and f : Y → Z is continuous with Y dense in XI , several natural questions arise: (a) does f depend on some small J ⊆ I? (b) if it does, when is fJ continuous? (c) if fJ is continuous, when does it extend to continuous fJ : XJ → Z? (d) if fJ so extends, when does f extend to continuous f : XI → Z? (e) if f depends on some J ⊆ I and f extends to continuous f : XI → Z, when does f also depend on J? The authors offer answers (some complete, some partial) to some of these questions, together with relevant counterexamples. Theorem 1. f has a continuous extension f : XI → Z that depends on J if and only if fJ is continuous and has a continuous extension fJ : XJ → Z. Example 1. For ω ≤ k ≤ c there are a dense subset Y of [0, 1]k and f ∈ C(Y, [0, 1]) such that f depends on every nonempty J ⊆ k, there is no J ∈ [k]<ω such that fJ is continuous, and f extends continuously over [0, 1]k. Example 2. There are a Tychonoff space XI, dense Y ⊆ XI, f ∈ C(Y ), and J ∈ [I]<ω such that f depends on J, πJ [Y ] is C-embedded in XJ , and f does not extend continuously over XI .

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