Countable discrete extensions of compact lines

Speaker(s)

Grzegorz Plebanek

Affiliation

University of Wrocław

Date

May 24, 2023, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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We consider a separable compact line K and its extension L consisting of K and a countable number of 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 which norm is an odd natural number. We prove that if the topological weight of K is bigger than or equal to the least cardinality of a subset X of [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.
Based on the recent preprint https://arxiv.org/abs/2305.04565

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