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Pringle, Stephen (author), Davies, Zoe G. (author), Goddard, Mark A. (author), Dallimer, Martin (author), Hart, Emma (author), Le Goff, Léni E. (author), Langdale, Simon J. (author), Abad, Sara-Adela (author), Hamaza, S. (author)
report 2023
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Dow, Alan (author), Hart, K.P. (author), van Mill, J. (author), Vermeer, J. (author)
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 N. <br/>
journal article 2023
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Bellini, Matheus K. (author), Hart, K.P. (author), Rodrigues, Vinicius O. (author), Tomita, Artur H. (author)
We prove that if there are c incomparable selective ultrafilters then, for every infinite cardinal κ such that κ<sup>ω</sup>=κ, there exists a group topology on the free Abelian group of cardinality κ without nontrivial convergent sequences and such that every finite power is countably compact. In particular, there are arbitrarily large...
journal article 2023
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Dow, Alan (author), Hart, K.P. (author)
We present an example of a zero-dimensional F-space that is not strongly zero-dimensional.
journal article 2022
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Hart, K.P. (author), Dow, Alan (author)
The Proper Forcing Axiom implies that compact Hausdorff spaces are either first-countable or contain a converging ω1-sequence.
journal article 2022
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Jansen, A.J. (author), van Vlaardingen, A. (author), Choppin, S.B. (author), Hart, J (author), Litzenberger, S. (author), Schwanitz, S. (author), de Zee, M. (author), Madeleine, P. (author)
conference paper 2022
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Hart, K.P. (author)
journal article 2022
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Hart, K.P. (author), van Mill, J. (author)
We study the existence of universal autohomeomorphisms of N <sup>*</sup>. We prove that the Continuum Hypothesis (CH) implies there is such an auto-homeomorphism and show that there are none in any model where all auto-homeomorphisms of N <sup>*</sup> are trivial.
journal article 2022
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Hart, K.P. (author)
This paper looks at an argument in 'On the vastness of Natural Languages' by D. T. Langendoen and P. M. Postal.<br/><br/>The conclusion is that it does not pass mathematical muster.<br/><br/>The salient points are<br/><br/> saying "language rules impose no size limits" does not mean that one can say "there are arbitrarily large entities"; it...
working paper 2021
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Hart, K.P. (author), Hrusák, M (author), Verner, Jonathan (author)
This article is a reflection on the mathematical legacy of Professor Petr Simon.<br/><br/>
journal article 2020
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Hart, K.P. (author)
Een beschouwing naar aanleiding van het artikel 0,999 . . . = 1?<br/>van Jos Groot, Euclides 95 (3). 18–20. Met als conclusie dat het antwoord op<br/>de impliciete vraag natuurlijk “Ja” is.
journal article 2020
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Hart, K.P. (author)
In January 2019 the journal Nature reported on an exciting development in Machine Learning: the very first issue of the journal Nature Machine Intelligence contains a paper that describes a learning problem whose solvability is neither provable nor refutable on the basis of the standard ZFC axioms of Set Theory. In this note K. P. Hart describes...
journal article 2019
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Hart, K.P. (author)
The Katowice Problem is well known among topologists and set theorists. The aim of this paper is to make it known among analysts and to give Ben de Pagter something to think about in his retirement.
book chapter 2019
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Li, Y. (author), Vardon, P.J. (author), Hicks, M.A. (author), Hart, Jaap (author), Fokker, Peter A. (author)
OPERA-PU-TUD321d<br/>Radioactive substances and ionizing radiation are used in medicine, industry, agriculture, re- search, education and electricity production. This generates radioactive waste. In the Netherlands, this waste is collected, treated and stored by COVRA (Centrale Organisatie Voor Radioactief Afval). After interim storage for a...
report 2018
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Hart, K.P. (author), van Mill, J. (author)
The classical Erdös spaces are obtained as the subspaces of real sep- arable Hilbert space consisting of the points with all coordinates rational or all coordinates irrational, respectively. One can create variations by specifying in which set each coordinate is allowed to vary. We investigate the homogeneity of the resulting subspaces. Our...
journal article 2018
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Hart, K.P. (author)
This note is a somewhat personal account of a paper that L.E.J. Brouwer published in 1908 and that dealt with the possible cardinalities of subsets of the continuum. That paper is of interest because it represents the first time that Brouwer presented his ideas on foundations in an international forum. I found Brouwer's notions and arguments...
journal article 2018
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Yuan, Jun (author), Vardon, P.J. (author), Hicks, M.A. (author), Hart, J (author), Fokker, PA (author)
OPERA-PU-TUD321b<br/>Radioactive substances and ionizing radiation are used in medicine, industry, agriculture, re- search, education and electricity production. This generates radioactive waste. In the Neth- erlands, this waste is collected, treated and stored by COVRA (Centrale Organisatie Voor Radioactief Afval). After interim storage for a...
report 2017
document
Vardon, P.J. (author), Buragohain, Poly (author), Hicks, M.A. (author), Hart, J (author), Fokker, PA (author), Graham, C (author)
OPERA-PU-TUD321c<br/>Radioactive substances and ionizing radiation are used in medicine, industry, agriculture, re- search, education and electricity production. This generates radioactive waste. In the Neth- erlands, this waste is collected, treated and stored by COVRA (Centrale Organisatie Voor Radioactief Afval). After interim storage for a...
report 2017
document
Yuan, Jun (author), Vardon, P.J. (author), Hicks, M.A. (author), Hart, J (author), Fokker, PA (author)
Radioactive substances and ionizing radiation are used in medicine, industry, agriculture, re- search, education and electricity production. This generates radioactive waste. In the Neth- erlands, this waste is collected, treated and stored by COVRA (Centrale Organisatie Voor Radioactief Afval). After interim storage for a period of at least 100...
report 2017
document
Dow, A. (author), Hart, K.P. (author)
We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ?-sequence or a non-trivial converging ?1-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of...
journal article 2014
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