301 research outputs found
The Ho-Zhao problem
No full textGiven a poset P, the set Γ(P) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not. Ho & Zhao (2009) asked whether the category DCPO of dcpos is Γ-faithful. In this paper, we answer this question in the negative by exhibiting a counterexample. To achieve this, we introduce a new subcategory of dcpos which is Γ-faithful. This subcategory subsumes all currently known Γ-faithful subcategories. With this new concept in mind, we construct the desired counterexample which relies heavily on Johnstone’s famous dcpo which is not sober in its Scott topology
Topological Scott Convergence Theorem
No full textRecently, J. D. Lawson encouraged the domain theory community to consider the
scientific program of developing domain theory in the wider context of
spaces instead of restricting to posets. In this paper, we respond to this
calling with an attempt to formulate a topological version of the Scott
Convergence Theorem, i.e., an order-theoretic characterisation of those posets
for which the Scott-convergence is topological. To do this, we
make use of the replacement principle to create topological
analogues of well-known domain-theoretic concepts, e.g.,
-continuous spaces correspond to continuous posets, as
-convergence corresponds to -convergence. In this
paper, we consider two novel topological concepts, namely, the
-stable spaces and the spaces, and as a result we
obtain some necessary (respectively, sufficient) conditions under which the
convergence structure is topological
CUHK electronic theses & dissertations collection
No full textHo, Kin Tat.Thesis M.Phil. Chinese University of Hong Kong 2015.Includes bibliographical references (leaves 64-70).Abstracts also in Chinese.Title from PDF title page (viewed on 21, September, 2016)
Strong completions of spaces
No full textThis is an unpublished manuscript archived in Arxiv, available online at https://arxiv.org/pdf/1607.04162.pdfA non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible, (2) directed subsets (which of fundamental status in domain theory) of a poset are exactly its Alexandroff irreducible sets, (3) directed subsets (with respect to the specialization order) of a T0 space are always irreducible, and (4) the topological closure of every irreducible set is again irreducible. In recent years, the usefulness of irreducible sets in domain theory and non-Hausdorff topology has expanded. Notably, Zhao and Ho (2009) developed the core of domain theory directly in the context of T0 spaces by choosing the irreducible sets as the topological substitute for directed sets. Just as the existence of suprema of directed subsets is featured prominently in domain theory (and hence the notion of a dcpo – a poset in which all directed suprema exist), so too is that of irreducible subsets in the topological domain theory developed by Zhao and Ho. The topological counterpart of a dcpo is thus this: A T0 space is said to be strongly complete if the suprema of all irreducible subsets exist. In this paper, we show that the category, scTop+, of strongly complete To spaces forms a reflective subcategory of a certain lluf subcategory, Top+, of To spaces
The literary style of Ho Nai Kin’s writings (pdf berbeza)
No full textThe literary style is a combination of the nature of both creative subject and object, which presented in a perfect written work with distinctive and unique aesthetic pattern. The aesthetic value and significance of literary writing style of an author are the overall style and artistic features of his/her literary works. However, the multiformity between the innate character of an author and his/her scope of action, with the addition of author on different objects have different flexibility and selectivity, lead to the various styles of literary works. Ho Nai Kin (1946-2014) has been writing for more than 50 years, and his poetry and prose have peculiar originality. He is skilled at image capture and understand the natural world, and, through the blending of techniques in terms of rhetoric and representation, creating a poetic essay. His prose and poetry is full of creative imagination and unique expression, which mold his unique literary style, and laid his position in the history of Malaysian Chinese literature. With this in mind, the researcher attempts to investigate the literary style of Ho Nai Kin’s writings, and the scope of research will be the prose and poetry (except science and critical writings) of Ho Nai Kin within the year of 1965 to 2014. By clarifying the creative thinking of Ho Nai Kin via the intrinsic and extrinsic form of his writing, which are the contents and methods of artistic expression of the texts, it provides a better insight on the writer’s writing qualities. On the other hand, identify the value of his prose and poetry
An Operational Domain-theoretic Treatment of Recursive Types
No full textAbstractWe develop a domain theory for treating recursive types with respect to contextual equivalence. The principal approach taken here deviates from classical domain theory in that we do not produce the recursive types via the usual inverse limits constructions - we have it for free by working directly with the operational semantics. By extending type expressions to endofunctors on a 'syntactic' category, we establish algebraic compactness. To do this, we rely on an operational version of the minimal invariance property. In addition, we apply techniques developed herein to reason about FPC programs
LEARNING THROUGH “PLANE PUNCTUALITY”
No full textThe prompt service of in- and out-bound flights has made Changi Airport one of the best airports in the world. This chapter showcases how modelling tasks can be woven into the rich fabric of real-life contexts, that is familiar to Singapore students.Accepted versio
CUHK electronic theses & dissertations collection
No full textYeung, Kin Ho.Thesis M.Phil. Chinese University of Hong Kong 2014.Includes bibliographical references (leaves 255-271).Abstracts also in Chinese.Title from PDF title page (viewed on 21, December, 2016)
Operational domain theory and topology of sequential functional languages
No full textEThOS - Electronic Theses Online ServiceGBUnited Kingdo
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