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Compact productivity of Lindelöf-type properties
A subclass of the class of feebly Lindelöf spaces, namely the almost cellular-Lindelöf spaces, which contains the class of all cellular-Lindelöf...
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Adjoining a Strong Unit to an Archimedean Lattice-Ordered Group
Within archimedean ℓ -groups, “ G ∈ S W ∗ ” means there are H with strong unit ( H ∈ W ∗ ) and an embedding G ≤ H . A. Theorem (6.1) . For X a Tychonoff space...
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Categories of Locally Hypercompact Spaces and Quasicontinuous Posets
A subset of a topological space is hypercompact if its saturation (the intersection of its neighborhoods) is generated by a finite set. Locally...
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Proximity Frames and Regularization
It is well known that the category
KHaus of compact Hausdorff spaces is dually equivalent to the categoryKRFrm of compact regular frames. By de... -
Ultracompleteness of hyperspaces of compact sets
A space X is called ultracomplete if it has countable character in its Stone–Čech compactification βX . A space X is called almost locally compact if...
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Absorptive continuous ℝ-group actions on locally compact spaces
We introduce the notion of an ℝ-group of which the classical groups ℝ, ℤ and ℝ
+ * are typical examples, and we study flows ( X , ℋ), where X is a... -
Ends and quasicomponents
Let X be a connected locally compact metric space. It is known that if X is locally connected, then the space of ends (Freudenthal ends), EX , can be...
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Stability of homomorphisms in the compact-open topology
We will prove a kind of stability result for homomorphisms from locally compact to completely regular topological universal algebras with respect to...
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A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. II
This paper is a continuation of [7], where a duality theorem for the category HLC of locally compact Hausdorff spaces and continuous maps is proved....
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Remainders in extensions and finite unions of locally compact sets
We discuss the relationship between properties of spaces and their remainders in extensions from the class P fin of all finite unions of locally...
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A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. I
Generalizing de Vries’ duality theorem [9], we prove that the category HLC of locally compact Hausdorff spaces and continuous maps is dual to the...
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Covering properties which, under weak diamond principles, constrain the extents of separable spaces
We show that separable, locally compact spaces with property (a) necessarily have countable extent — i.e., have no uncountable closed, discrete...
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Topological representations of distributive hypercontinuous lattices
The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive...
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A Generalization of De Vries Duality Theorem
Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of locally compact Hausdorff spaces and...
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Transfinite Diameter, Chebyshev Constant and Energy on Locally Compact Spaces
We study the relationship between transfinite diameter, Chebyshev constant and Wiener energy in the abstract linear potential analytic setting...
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Supercomplete topological spaces
Supercomplete topological spaces and other variants of supercompleteness are defined in this paper. The main idea is to give different...
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Quasicontinuity of Posets via Scott Topology and Sobrification
In this paper, posets which may not be dcpos are considered. In terms of the Scott topology on posets, the new concept of quasicontinuous posets is...
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Choiceless, Pointless, but not Useless: Dualities for Preframes
We provide the appropriate common ‘(pre)framework’ for various central results of domain theory and topology, like the Lawson duality of continuous...