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K. P. Hart

Publications and source records attributed to K. P. Hart.

7 recordsLinked to original sources
arXiv2021

Countably compact group topologies on arbitrarily large free Abelian groups

We prove that if there are $\mathfrak c$ incomparable selective ultrafilters then, for every infinite cardinal $κ$ such that $κ^ω=κ$, 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 countably compact groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.

math.LO↗
arXiv2005

A note on an example by van Mill

Improving on an earlier example by J. van Mill, we prove that there exists a zero-dimensional compact space of countable pi-weight and uncountable character which is homogeneous under MA+notCH, but not under CH.

math.GN↗
arXiv2004

Span, chainability and the continua H* and I_u

We show that the continua I_u and H* are non-chainable and have span nonzero. Under CH this can be strengthened to surjective symmetric span nonzero. We discuss the logical consequences of this.

math.GN↗
arXiv2001

Embeddings into P(N)/fin and extension of automorphisms

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 show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

math.LO↗
arXiv2001

On the Ma\'{c}kowiak-Tymchatyn theorem

In this paper we give new proofs of the theorem of Ma\'{c}kowiak and Tymchatyn that every metric continuum is a weakly-confluent image of some one-dimensional hereditarily indecomposable continuum of countable weight. The first is a model-theoretic argument; the second is a topological proof inspired by the first.

math.GN↗