3 citations · 12 across the 17 of their papers we have counts for
22 papers
World Potential Model: Pretrained World Knowledge as Progress Potentials
Jun Zhao, Jixin Tang, Yang Shu +6
Long-horizon language agents often receive supervision only from terminal task outcomes, leaving little signal for distinguishing productive intermediate behavior from stagnation o…
-embedding, Lindelöfness, and Čech-completeness
Alan Dow, Klaas Pieter Hart, Jan van Mill +1
We show that in the class of Lindelöf Čech-complete spaces the property of being -embedded is quite well-behaved. It admits a useful characterization that can be used to show th…
Buried points of plane continua
David Lipham, Jan van Mill, Murat Tuncali +2
Sets on the boundary of a complementary component of a continuum in the plane have been of interest since the early 1920's. Curry and Mayer defined the buried points of a plane con…
Nowhere constant families of maps and resolvability
István Juhász, Jan van Mill
If is a topological space and is any set then we call a family of maps from to nowhere constant if for every non-empty open set in there is $f…
Homogeneous continuous images of smaller weight
István Juhász, Jan van Mill
We show that every infinite crowded space can be mapped onto a homogeneous space of countable weight, and that there is a homogeneous space of weight continuum that cannot be mappe…
On Shehtman's Two Problems
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan +1
We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the Čech-Stone compactification of an ordinal space. We use the Continuum Hypothesis to…
Closed copies of in
Alan Dow, Klaas Pieter Hart, Jan van Mill +1
We investigate closed copies of~ in powers of~ with respect to - and -embedding. We show that contains closed copies of~$\mathbb{…
On the double density spectra of compact spaces
István Juhász, Jan Van Mill
The set of densities of all dense subspaces of a topological space is called the double density spectrum of . In this note we present a couple of results that imply…
Some realcompact spaces
Alan Dow, Jan van Mill, Klaas Pieter Hart +1
We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of the space of natural numbers.
Problems on
Klaas Pieter Hart, Jan van Mill
This is an update on, and expansion of, our paper Open problems on in the book Open Problems in Topology.
The double density spectrum of a topological space
Istvan Juhasz, Jan van Mill, Lajos Soukup +1
It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the s…
Universal autohomeomorphisms of
Klaas Pieter Hart, Jan van Mill
We study the existence of universal autohomeomorphisms of . We prove that implies there is such an autohomeomorphism and show that there are none in any…
Conjugacy classes of autohomeomorphisms of
Klaas Pieter Hart, Jan van Mill
We present some problems related to the conjugacy classes of .
Actions of semitopological groups
Jan van Mill, Vesko Valov
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
Compactifiable classes of compacta
A. Bartoš, J. Bobok, J. van Mill +2
We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizabl…
Infinite powers and Cohen reals
Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy
We give a consistent example of a zero-dimensional separable metrizable space such that every homeomorphism of acts like a permutation of the coordinates almost everywher…
Alan Dow
Klaas Pieter Hart, Jan van Mill
On the occasion of Alan Dow 60th birthday.
A homogeneous space whose complement is rigid
Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy
We construct a homogeneous subspace of whose complement is dense in and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homog…
A short proof of Toruńczyk's Characterization Theorems
Jan J. Dijkstra, Michael Levin, Jan van Mill
We present short proofs of Toruńczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.
Unions of F-spaces
Klaas Pieter Hart, Leon Luo, Jan van Mill
We show that every space that is the union of a `small' family consisting of special P-sets that are F-spaces, is an F-space. We also comment on the sharpness of our results.
Covering dimension and finite-to-one maps
Klaas Pieter Hart, Jan van Mill
Hurewicz' characterized the dimension of separable metrizable spaces by means of finite-to-one maps. We investigate whether this characterization also holds in the class of compact…
Embeddings into P(N)/fin and extension of automorphisms
A. Bella, A. Dow, K. P. Hart +3
Given a Boolean algebra B and an embedding e:B -> P(N)/fin we consider the possibility of extending each or some automorphism of B to the whole P(N)/fin. Among other things, we sho…