Function spaces on separable compact lines

Speaker(s)

Kacper Kucharski

Affiliation

Doctoral School of Exact and Natural Sciences UW

Language of the talk

Polish

Date

April 15, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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A compact line is any linearly ordered compact topological space. During the talk we will provide a complete isomorphism classification of the spaces of real-valued continuous functions endowed with the topology of pointwise convergence $C_p(K)$ for separable compact lines $K$ of weight $\omega_1$, under the assumption of the Baumgartner's axiom BA. In particular, we will show that, up to linear homeomorphism, there are exactly three function spaces $C_p(K)$, for such $K$. This result should be compared with the recent work of Korpalski, Koszmider and Marciszewski in which it was proven that under the assumption of BA, whenever $K$ and $L$ are separable compact lines of weight $\omega_1$, then the Banach spaces $C(K)$ and $C(L)$ are isomorphic.
Next, we will construct a ZFC example of a separable compact line $K$ of weight $2^{\omega}$, whose spaces of continuous functions with the pointwise convergence topology $C_p(K)$ and the weak topology $C_w(K)$ are not homeomorphic to their square.

 

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