Alan Dow

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math.GN2025

All spaces of countable spread can be small

Alan Dow, IstvÃ¡n JuhÃ¡sz

The main result of this paper is the proof of the simultaneous consistency, modulo a weakly compact cardinal, of the equality $2^{< c} = c$ with the following…

math.GN2025

New examples in the study of selectively separable spaces

Alan Dow, Hayden Pecoraro

The property of being selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomsk…

math.GN2025

Sequentially compact separable spaces

Cesar Corral, Alan Dow, Paul Szeptycki

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

math.GN2025

Not OCA and products of Frechet spaces

Alan Dow

We continue the investigation of the question of whether the product of two countable FrÃ©chet spaces must be M-separable. We are especially interested in this question in the pres…

math.GN2024

Autohomeomorphisms of pre-images of $N^{*}$

Alan Dow

In the study of the Stone-uCech remainder of the real line a detailed study of the Stone-uCech remainder of the space $N \times [0, 1]$ , which we denote as $M$ , has o…

math.GN2024

Non-trivial copies of N*

Alan Dow

We show that it is consistent to have regular closed non-clopen copies of $N^{*}$ within $N^{*}$ and a non-trivial self-map of $N^{*}$ even if all autohomeomorphi…

All spaces of countable spread can be small

New examples in the study of selectively separable spaces

Sequentially compact separable spaces

Not OCA and products of Frechet spaces

Autohomeomorphisms of pre-images of N∗

Non-trivial copies of N*

Autohomeomorphisms of pre-images of $N^{*}$