Monotone insertion of continuous functions

Good, Chris; Stares, Ian

doi:10.1016/s0166-8641(99)00122-4

Cited by 19 publications

(14 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth mentioning Borges [4,5] for a characterization of monotone normality via a monotone Urysohn's lemma. Later on, Good and Stares [12] and Lane, Nyikos and Pan [22] studied monotone versions of Dowker and Michael's theorems. Surprisingly, both results characterize stratiable spaces (which consequently can be seen as monotonically perfectly normal spaces).…”

Section: Introductionmentioning

confidence: 99%

Monotone insertion of lattice-valued functions

Mardones-Pérez

Vicente

2007

Acta Math Hung

View full text Add to dashboard Cite

Insertion of lattice-valued functions in a monotone manner is investigated. For L a -separable completely distributive lattice (i.e. L admits a countable base which is free of supercompact elements), a monotone version of the Kat¥tovTong insertion theorem for L-valued functions is established. We also provide a monotone lattice-valued version of Urysohn's lemma. Both results yield new characterizations of monotonically normal spaces. Moreover, extension of lattice-valued functions under additional assumptions is shown to characterize also monotone normality.

show abstract

Section: Introductionmentioning

confidence: 99%

Monotone insertion of lattice-valued functions

Mardones-Pérez

Vicente

2007

Acta Math Hung

View full text Add to dashboard Cite

show abstract

“…A space is stratifiable if and only there is an operator U assigning an open set U (n, D) to every closed set D and n ∈ N such that n∈N U (n, D) = D and U (n, D) ⊆ U (n, D ) whenever D ⊆ D . The following two results appear in [7] (see also [6]) and [20] respectively. One can also prove these results from Kubiak's in exactly the same way as Dowker's and Michael's follow from the Katětov-Tong Theorem so we omit the proofs here.…”

Section: Proofmentioning

confidence: 91%

Interpolating functions

Good

Kopperman

Yıldız

2011

Topology and its Applications

Self Cite

View full text Add to dashboard Cite

Let X, Y be sets with quasiproximities X and Y (where A B is interpreted as "B is a neighborhood of A"). Let f , g : X → Y be a pair of functions such that whenever C Y D,whenever C Y D, is continuous, many classical "sandwich" or "insertion" theorems are corollaries of this result. The paper is written to emphasize the strong similarities between several concepts• the posets with auxiliary relations studied in domain theory; • quasiproximities and their simplification, Urysohn relations; and • the axioms assumed by Katětov and by Lane to originally show some of these results.Interpolation results are obtained for continuous posets and Scott domains. We also show that (bi-)topological notions such as normality are captured by these order theoretical ideas.

show abstract

“…mapping φ u and an l.s. On (3), (3) and (3) , "φ : X → C c (R)", "φ : X → C(R)" and "φ : X → C(Y )" cannot be replaced by "φ : X → F c (R)", "φ : X → F(R)" and "φ : X → F(Y )", respectively, to characterize monotonically normal spaces X. For, assume on the contrary, if we consider the conditions modifying as in the above, each of them implies that X is…”

Section: By Using G(a B)∩((ψ (mentioning

confidence: 99%

“…Let Φ and Ψ be operators as in(3). For every pair (A, B) of disjoint closed subsets of X, define a u.s.c.…”

mentioning

confidence: 99%