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Journals and Conferences
Let X be a non-empty set. By O(X) we denote the set of all finitary operations on X, i.e. all functions X → X of arbitrary arity n. A clone on X is a subset of O(X) which contains all projections, i.e. all mappings (x1, . . . , xn) 7→ xi for arbitrary 1 ≤ i ≤ n, and which is closed under superposition, i.e. together with f : X → X and g1, . . . , gn : X m →… (More)
On an infinite base set X, every ideal of subsets of X can be associated with the clone of those operations on X which map small sets to small sets. We continue earlier investigations on the position of such clones in the clone lattice.
We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present… (More)
Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that A' is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets. Then it is proved that each countable Boolean algebra has the… (More)
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.
Throughout this paper X denotes a compact and zero-dimensional Hausdorr space. We shall be concerned with Theorem 0.1 The following assertions are equivalent. (A) X is the continuous image of a compact ordered space. (B) X is the continuous image of a zero-dimensional compact ordered space. (C) X has a T 0-separating cross-free family of clopen sets. (D) X… (More)
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.