Given a Boolean algebra B and an embedding e:B -> P(N)/fin we consider the possibility of exte... more 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.
We show that Lelek's problem on the chainability of continua with span zero is not a metric p... more We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
Our main results are: (1) after adding any number of Cohen reals to a model of GCH the space U(o,... more Our main results are: (1) after adding any number of Cohen reals to a model of GCH the space U(o,> is co-absolute with a power of w2 and there is a model in which U(o,) is not co-absolute with any product of discrete spaces.
We prove that if every family in ( ω ω, ≤ * ) of size less than c is bounded then there exists a ... more We prove that if every family in ( ω ω, ≤ * ) of size less than c is bounded then there exists a point p in Q * such that p generates an ultrafilter in the set-theoretic sense on Q and such that p has a base consisting of sets that are homeomorphic to Q. This is a partial answer to Question 30 (Problem 229) in .
In this paper we show that, when we iteratively add Sacks reals to a model of ZF C we have for ev... more In this paper we show that, when we iteratively add Sacks reals to a model of ZF C we have for every two reals in the extension a continuous function defined in the ground model that maps one of the reals onto the other.
We show that Lelek's problem on the chainability of continua with span zero is not a metric probl... more We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
We show that the continua Iu and H∗ are nonchainable and have span nonzero. Under CH this can be ... more We show that the continua Iu and H∗ are nonchainable and have span nonzero. Under CH this can be strengthened to surjective symmetric span nonzero.We discuss the logical consequences of this.
Steprāns provided a characterization of βN\N in the ℵ 2 -Cohen model that is much in the spirit o... more Steprāns provided a characterization of βN\N in the ℵ 2 -Cohen model that is much in the spirit of Parovičenko's characterization of this space under CH. A variety of the topological results established in the Cohen model can be deduced directly from the properties of βN\N or P(N)/fin that feature in Steprāns' result. : S 0 1 6 6 -8 6 4 1 ( 0 1 ) 0 0 1 3 8 -9 S = {a ∈ A α : a < a α } and T = a ∈ A α : a < a α .
Martin's Axiom for σ-centered partial orders implies that there is a cosmic space with non-coinci... more Martin's Axiom for σ-centered partial orders implies that there is a cosmic space with non-coinciding dimensions.
It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizabl... more It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable π-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character.
Atlas home || Conferences | Abstracts | about Atlas The 1997 Spring Topology and Dynamics Confere... more Atlas home || Conferences | Abstracts | about Atlas The 1997 Spring Topology and Dynamics Conference April 10-12, 1997 University of Southwestern Louisiana Lafayette, LA, USA. Organizers Bradd Clark, Kathleen Lopez, Vic Schneider, Roger Waggoner, Thelma West. Abstracts. Gerardo Acosta-Garcia Continua Which Have The Property of Kelley Hereditarily RD Anderson Is There Life After Topology? Valerio De Angelis Distribution of Small ...
Abstract. We recall a characterization of hereditary indecomposability orig- inally obtained by K... more Abstract. We recall a characterization of hereditary indecomposability orig- inally obtained by Krasinkiewicz and Minc, and show how it may be used to give unified constructions of various hereditarily indecomposable continua. In ...
Given a Boolean algebra B and an embedding e:B -> P(N)/fin we consider the possibility of exte... more 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.
We show that Lelek's problem on the chainability of continua with span zero is not a metric p... more We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
Our main results are: (1) after adding any number of Cohen reals to a model of GCH the space U(o,... more Our main results are: (1) after adding any number of Cohen reals to a model of GCH the space U(o,> is co-absolute with a power of w2 and there is a model in which U(o,) is not co-absolute with any product of discrete spaces.
We prove that if every family in ( ω ω, ≤ * ) of size less than c is bounded then there exists a ... more We prove that if every family in ( ω ω, ≤ * ) of size less than c is bounded then there exists a point p in Q * such that p generates an ultrafilter in the set-theoretic sense on Q and such that p has a base consisting of sets that are homeomorphic to Q. This is a partial answer to Question 30 (Problem 229) in .
In this paper we show that, when we iteratively add Sacks reals to a model of ZF C we have for ev... more In this paper we show that, when we iteratively add Sacks reals to a model of ZF C we have for every two reals in the extension a continuous function defined in the ground model that maps one of the reals onto the other.
We show that Lelek's problem on the chainability of continua with span zero is not a metric probl... more We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
We show that the continua Iu and H∗ are nonchainable and have span nonzero. Under CH this can be ... more We show that the continua Iu and H∗ are nonchainable and have span nonzero. Under CH this can be strengthened to surjective symmetric span nonzero.We discuss the logical consequences of this.
Steprāns provided a characterization of βN\N in the ℵ 2 -Cohen model that is much in the spirit o... more Steprāns provided a characterization of βN\N in the ℵ 2 -Cohen model that is much in the spirit of Parovičenko's characterization of this space under CH. A variety of the topological results established in the Cohen model can be deduced directly from the properties of βN\N or P(N)/fin that feature in Steprāns' result. : S 0 1 6 6 -8 6 4 1 ( 0 1 ) 0 0 1 3 8 -9 S = {a ∈ A α : a < a α } and T = a ∈ A α : a < a α .
Martin's Axiom for σ-centered partial orders implies that there is a cosmic space with non-coinci... more Martin's Axiom for σ-centered partial orders implies that there is a cosmic space with non-coinciding dimensions.
It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizabl... more It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable π-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character.
Atlas home || Conferences | Abstracts | about Atlas The 1997 Spring Topology and Dynamics Confere... more Atlas home || Conferences | Abstracts | about Atlas The 1997 Spring Topology and Dynamics Conference April 10-12, 1997 University of Southwestern Louisiana Lafayette, LA, USA. Organizers Bradd Clark, Kathleen Lopez, Vic Schneider, Roger Waggoner, Thelma West. Abstracts. Gerardo Acosta-Garcia Continua Which Have The Property of Kelley Hereditarily RD Anderson Is There Life After Topology? Valerio De Angelis Distribution of Small ...
Abstract. We recall a characterization of hereditary indecomposability orig- inally obtained by K... more Abstract. We recall a characterization of hereditary indecomposability orig- inally obtained by Krasinkiewicz and Minc, and show how it may be used to give unified constructions of various hereditarily indecomposable continua. In ...
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