P. Szeptycki

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math.GN2025

Normality in the square of the Sorgenfrey Line

Paul Szeptycki, Hongwei Wen

We consider sets of reals $X$ endowed with the Sorgenfrey lower limit topology denoted $X [\leq]$ . Przymusiński proved that if $X$ is a $Q$ -set then $(X [\leq])^{2}$ is normal. While t…

math.GN2025

Sequentially compact separable spaces

Cesar Corral, Alan Dow, Paul Szeptycki

We consider the following variation of the Scarborough-Stone problem: Is $X^{κ}$ always countably compact whenever $X$ is separable and sequentially compact?

math.GN2025

Q-Sets, Δ-Sets, and L-Spaces

Pourya Memarpanahi, Paul Szeptycki

The question whether there is a Lindelof Q-set space or Lindelof $Δ$ -set space is considered. We show that J. Moore's ZFC $L$ -space is not a Q-set space in ZFC and, assuming all Ar…