J. Mill

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math.GN2025

Condensations with extra properties

IstvÃ¡n JuhÃ¡sz, Jan van Mill, Lajos Soukup

We show that there are locally compact spaces that can be condensed onto separable spaces but not onto compact separable spaces. We also show that for every cardinal $I^º$ there is…

math.GN2025

A universal $P$ -group of weight $ℵ$

Jan van Mill

We show that under the Continuum Hypothesis, the topological group of all homeomorphisms of the Äech-Stone remainder of $I ¨ $ with the $G_{I^} ´$ -topology, is a universal object for al…

math.GN2025

Some new results on $I^$ -spaces

I. JuhÃ¡sz, J. van Mill, L. Soukup +1

A topological space $X$ is a $I^$ -space (or $X \in I^$ ) if for any decreasing sequence ${A_{n} : n < I ¨ }$ of subsets of $X$ with empty intersection there is a (decreasing) sequence…

math.GN2024

Countable tightness is not discretely reflexive in $I ¨ $ -compact spaces

IstvÃ¡n JuhÃ¡sz, Jan van Mill

Answering a question raised by V. V. Tkachuk, we present several examples of $I ¨ $ -compact spaces, some only consistent and some in ZFC, that are not countably tight but in which th…

math.GN2024

Problems on $I^^{2} N$

Klaas Pieter Hart, Jan van Mill

This is an update on, and expansion of, our paper Open problems on $I^^{2} I ¨ $ in the book Open Problems in Topology.

math.GN2024

$C$ -embedding, LindelÃ¶fness, and Äech-completeness

Alan Dow, Klaas Pieter Hart, Jan van Mill +1

We show that in the class of LindelÃ¶f Äech-complete spaces the property of being $C$ -embedded is quite well-behaved. It admits a useful characterization that can be used to show…

Condensations with extra properties

A universal P-group of weight ℵ

Some new results on I^-spaces

Countable tightness is not discretely reflexive in I¨-compact spaces

Problems on I^2N

C-embedding, LindelÃ¶fness, and Äech-completeness

A universal $P$ -group of weight $ℵ$

Some new results on $I^$ -spaces

Countable tightness is not discretely reflexive in $I ¨ $ -compact spaces

Problems on $I^^{2} N$

$C$ -embedding, LindelÃ¶fness, and Äech-completeness