Local extension property for finite height spaces

Correa, Claudia; Tausk, Daniel V.

doi:10.4064/fm513-6-2018

Search citation statements

Order By: Relevance

Paper Sections

Select...

Outside (E)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2024

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the light of results on twisted sums from [18,8,3], the following generalization of Problem 1.3 seems to be worth considering.…”

Section: Outside (E)mentioning

confidence: 99%

Countable discrete extensions of compact lines

Korpalski,

Plebanek

2024

Fund. Math.

View full text Add to dashboard Cite

We consider a separable compact line K and its extension L consisting of K and countably many isolated points. The main object of study is the existence of a bounded extension operator E : C(K) → C(L). We show that if such an operator exists, then there is one for which ∥E∥ is an odd natural number. We prove that if the topological weight of K is greater than or equal to the least cardinality of a set X ⊆ [0, 1] that cannot be covered by a sequence of closed sets of measure zero, then there is an extension L of K admitting no bounded extension operator.

show abstract

“…In the light of results on twisted sums from [18,8,3], the following generalization of Problem 1.3 seems to be worth considering.…”

Section: Outside (E)mentioning

confidence: 99%

Countable discrete extensions of compact lines

Korpalski,

Plebanek

2024

Fund. Math.

View full text Add to dashboard Cite

show abstract

Barely alternating real almost chains and extension operators for compact lines

Avilés,

Korpalski

2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

View full text Add to dashboard Cite

Assume $$\text {MA}(\kappa )$$ MA ( κ ) . We show that for every real chain of size $$\kappa $$ κ in the quotient Boolean algebra $$P(\omega )/fin$$ P ( ω ) / f i n we can find an almost chain of representatives such that every $$n\in \omega $$ n ∈ ω oscillates at most three times along the almost chain. This is used to show that for every countable discrete extension of a separable compact line K of weight $$\kappa $$ κ there exists an extension operator $$E:C(K)\longrightarrow C(L)$$ E : C ( K ) ⟶ C ( L ) of norm at most three.

show abstract