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Article
Correction to: Ultrafilter selection and corson compacta
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Article
Ultrafilter selection and Corson compacta
We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For ca...
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Article
Vietoris hyperspaces over scattered Priestley spaces
We study Vietoris hyperspaces of closed and final sets of Priestley spaces. We are particularly interested in Skula topologies. A topological space is Skula if its topology is generated by differences of open ...
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Article
Poset algebras over well quasi-ordered posets
A new class of partial order-types, class \({\mathcal{G}}^{+}_{bqo}\) is defined and investigated here. A poset P is ...
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Article
Chains of well-generated Boolean algebras whose union is not well-generated
A Boolean algebraB that has a well-founded sublattice which generatesB is called awell-generated Boolean algebra. Every well-generated Boolean algebra is superatomic. However, there are superatomic algebras which...
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Article
On poset Boolean algebras of scattered posets with finite width
We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.
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Article
On a poset algebra which is hereditarily but not canonically well generated
LetB be a superatomic Boolean algebra.B is well generated, if it has a well founded sublatticeL such thatL generatesB. The free product of Boolean algebrasB andC is denoted byB *C. IfC is a chain thenB(C) denotes...
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Article
On Poset Boolean Algebras
Let (P,≤) be a partially ordered set. The poset Boolean algebra of P, denoted F(P), is defined as follows: The set of generators of F(P) is {x p : p∈P}, and the...
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Article
On a superatomic Boolean algebra which is not generated by a well-founded sublattice
Let b denote the unboundedness number of ωω. That is, b is the smallest cardinality of a subset \(F \subseteq \omega ^\omega \) ...
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Article
On HCO spaces. An uncountable compactT 2 space, different from ℵ1+1, which is homeomorphic to each of its uncountable closed subspaces, which is homeomorphic to each of its uncountable closed subspaces
LetX be an Hausdorff space. We say thatX is a CO space, ifX is compact and every closed subspace ofX is homeomorphic to a clopen subspace ofX, andX is a hereditarily CO space (HCO space), if every closed subspace...
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Chapter
On Superatomic Boolean algebras
Let us recall that a Boolean algebra B is superatomic if every homomorphic image is atomic. A Boolean algebra B is an interval algebra if there is a chain C having a first element, say 0 C ...
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Article
Compact interval spaces in which all closed subsets are homeomorphic to clopen ones, II
A topological spaceX whose topology is the order topology of some linear ordering onX, is called aninterval space. A space in which every closed subspace is homeomorphic to a clopen subspace, is called aCO space ...
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Article
Compact interval spaces in which all closed subsets are homeomorphic to clopen ones, I
A topological space X whose topology is the order topology of some linear ordering on X, is called an interval space. A space in which every closed subspace is homeomorphic to a clopen subspace, is called a CO sp...
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Article
Comparison of Boolean algebras
In this work, some results related to superatomic Boolean interval algebras are presented, and proved in a topological way. Let x be an uncountable cardinal. To each I
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Chapter and Conference Paper
On homomorphism types of superatomic interval Boolean algebras
Let Dκ be the class of superatomic interval Boolean algebras of cardinality κ ⩾ ω1. For κ ⩽ α < κ+ and for m,n < ω, m+n ⩾ 1, let Bα,m,n be the superatomic interval algebra generated by the chain ωα · m + (ωα*). n...
