K.P. Hart
53 records found
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 N.
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We prove that if there are c incomparable selective ultrafilters then, for every infinite cardinal κ such that κω=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 cou
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We present some problems related to the conjugacy classes of Aut(N^*).
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We present an example of a zero-dimensional F-space that is not strongly zero-dimensional.@en
We study the existence of universal autohomeomorphisms of N
*. 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
*
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De verzamelingenleer ontstond aan het eind van de negentiende eeuw toen Georg Cantor kwantitatieve vragen begon te stellen over deelverzamelingen van de getallenlijn. Het negatieve antwoord op de vraag "Zijn er evenveel natuurlijke als reële getallen?" zette aan tot dieper onderz
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It is shown that, assuming the Continuum Hypothesis, every compact Hausdorff space of weight at most c is a remainder in a soft compactification of N.
We also exhibit an example of a compact space of weight aleph_1 ---hence a remainder in some compactification of N ---f ...
We also exhibit an example of a compact space of weight aleph_1 ---hence a remainder in some compactification of N ---f ...
The Proper Forcing Axiom implies that compact Hausdorff spaces are either first-countable or contain a converging ω1-sequence.@en
This paper looks at an argument in 'On the vastness of Natural Languages' by D. T. Langendoen and P. M. Postal.
The conclusion is that it does not pass mathematical muster.
The salient points are
saying "language rules impose no size limits" does not mean that one can say
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This article is a reflection on the mathematical legacy of Professor Petr Simon.
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Een beschouwing naar aanleiding van het artikel 0,999 . . . = 1?
van Jos Groot, Euclides 95 (3). 18–20. Met als conclusie dat het antwoord op
de impliciete vraag natuurlijk “Ja” is.@en
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.@en
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 s
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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
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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.
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We prove that compact Hausdorff spaces with a PP-diagonal are metrizable. This answers problem 4.1 (and the equivalent problem 4.12) from Cascales et al. (2011).
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This article attempts to survey Alan Dow's contributions to General and Set-theoretic Topology.@en