Countable discrete extensions of compact lines
Tom 265 / 2024
Fundamenta Mathematicae 265 (2024), 75-93
MSC: Primary 54F05; Secondary 46B03, 06E15, 03E05
DOI: 10.4064/fm230613-25-1
Opublikowany online: 20 March 2024
Streszczenie
We consider a separable compact line 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)\to 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\subseteq [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.
