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Non-Hausdorff Topology and Domain Theory: Selected Topics in Point-Set Topology
TLDR
This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff, essential for domain theory, the cornerstone of semantics of computer languages.Abstract:
This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.read more
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A Wadge hierarchy for second countable spaces
TL;DR: A notion of reducibility for subsets of a second countable T0 topological space based on relatively continuous relations and admissible representations is defined and induces a hierarchy that refines the Baire classes and the Hausdorff–Kuratowski classes of differences.
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Full Abstraction for Non-Deterministic and Probabilistic Extensions of PCF I: the Angelic Cases
TL;DR: This work examines several extensions and variants of Plotkin's language PCF, including non-deterministic and probabilistic choice constructs, and gives an operational and a denotational semantics, and compares them.
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Variational principles, completeness and the existence of traps in behavioral sciences
TL;DR: This paper establishes new forward and backward versions of Ekeland’s variational principle for the class of strict-decreasingly forward-lsc functions in pseudo-quasimetric spaces and shows that the completeness of a space is equivalent to the existence of traps.
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Residuated implications derived from quasi-overlap functions on lattices
TL;DR: In this paper, the concept of residuated implications related to quasi-overlap functions on lattices was introduced, and the notion of densely ordered posets was used to generalize a classification theorem for residuated quasioverlaps.
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Theory of (q1, q2)-quasimetric spaces and coincidence points
TL;DR: In this paper, the existence of a coincidence point of two mappings acting between (q1, q2)-quasimetric spaces such that one is a covering mapping and the other satisfies the Lipschitz condition is investigated.