Musing on Kunen's compact $L$-space
Grzegorz Plebanek

TL;DR
This paper constructs a connected compact $L$-space extending Kunen's work under CH, revealing a Corson compact space with a Banach space of continuous functions not isomorphic to any on a zero-dimensional compactum.
Contribution
It introduces a connected version of Kunen's compact $L$-space, expanding understanding of the structure of Corson compact spaces and their associated Banach spaces.
Findings
Constructed a connected compact $L$-space under CH.
Identified a Corson compact space with unique Banach space properties.
Showed $C(K)$ is not isomorphic to any space of continuous functions on a zero-dimensional compactum.
Abstract
We present a connected version of the compact -space constructed by Kenneth Kunen under CH. We show that this provides a Corson compact space such that the Banach space is isomorphic to no space of continuous function on a zero-dimensional compactum.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Advanced Operator Algebra Research
