Core compactness of ordered topological spaces

Article Mathematics

Continuity and Directed Completion of Topological Spaces

Zhongxi Zhang et al.

Summary: This paper introduces the concepts of continuity, meet continuity, and quasicontinuity of Delta-spaces, and establishes the relationships between them. It also demonstrates that other continuity concepts can be regarded as special cases of Delta-space continuity. Additionally, it introduces the Scott completion as a type of directed completion for Delta-spaces.

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS (2022)

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Article Mathematics, Applied

Two topologies on the lattice of Scott closed subsets

Yu Chen et al.

Summary: This paper discusses the Scott topology and the lower Vietoris topology on a poset P, providing sufficient conditions for the two topologies to be equal. An adjunction between Σ(P) and Σ(Gamma(P)) is established, and properties regarding core-compactness and sobriety are demonstrated.

TOPOLOGY AND ITS APPLICATIONS (2022)

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Article Mathematics, Applied

Core-compactness, consonance and the Smyth powerspaces

Zhenchao Lyu et al.

Summary: We prove that the Smyth powerspace Q(S)(X) of a topological space X is core-compact if and only if X is locally compact. As a straightforward consequence, we obtain that the Smyth powerspace construction does not generally preserve core-compactness. Besides, we prove that Q(S)(X) is consonant implies that X is consonant and conversely that the Smyth powerspace construction preserves consonance under some additional conditions. Furthermore, we obtain necessary conditions as well as some sufficient conditions, under which the upper topology and upper Vietoris topology on the set of non-empty compact saturated subsets of X with the reverse inclusion order coincide.

TOPOLOGY AND ITS APPLICATIONS (2022)

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Article Mathematics

Compactness on Soft Topological Ordered Spaces and Its Application on the Information System

T. M. Al-shami

Summary: This study introduces new concepts of soft compactness by combining soft information systems and partially ordered sets, focusing on their applications in finite spaces. The research explores notions of monotonic soft sets, monotonic soft compactness, and ordered soft compact spaces, showing their interrelationships through examples. Complete descriptions are provided for each concept using the finite intersection property.

JOURNAL OF MATHEMATICS (2021)

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Article Mathematics, Applied