Is Every Partially Ordered Space with a Completely Regular Topology Already a Completely Regular Partially Ordered Space?

Schwarz, Friedhelm; Weck-Schwarz, Sibylle

doi:10.1002/mana.19931610114

Search citation statements

Order By: Relevance

Paper Sections

Select...

Remarks1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1993

2024

Publication Types

Select...

Article3

Book2

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 6 publications

(1 citation statement)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the following problem does not seem to have as simple a solution: For a partially ordered space to belong to CrPOTop, is it sufficient that the topology be Tychonoff? (This question was recently answered, in the negative, by S. WECK-SCHWARZ, see [37]. )…”

Section: Remarksmentioning

confidence: 99%

On the MacNeille Completion of the Category of Partially Ordered Topological Spaces

Schauerte

1993

Mathematische Nachrichten

View full text Add to dashboard Cite

Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the To( TI, T2) preordered spaces and the (completely regular) partially ordered spaces. We also show that a functor due to L. NACHBIN from the quasi-uniform spaces to the preordered spaces preserves initial sources.

show abstract

Section: Remarksmentioning

confidence: 99%