Euclidean metric frames which are not spatial
Feizabadi AK, Manafi M, Moghbeli H (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 87
Article Number: 35
Journal Issue: 4
DOI: 10.1007/s00012-026-00916-z
Abstract
In this paper, we employ the concept of a ζ-ideal J and introduce a quotient frame M(X,J), where X is a topological space. We prove that for a metric space X, this frame is metrizable. Moreover, a necessary and sufficient condition for spatiality of frame M(X,J) will be given. Finally, we apply this general case to the metric space Rn and construct frames which are metrizable but not spatial. More precisely, these frames are derived from the metric space Rn which are actually the quotients of frame O(Rn), the set of open subsets of Rn. The technique of constructing these frames, which are denoted by Mi(X,S), i=0,1,2, intuitively, is a process in which a given subset of points are removed.
Involved external institutions
Islamic Azad University, Gorgan Branch (IAU) / دانشگاه آزاد اسلامی واحد گرگان
Iran, Islamic Republic of (IR)
University of Jiroft / دانشگاه جیرفت
Iran, Islamic Republic of (IR)
Iran, Islamic Republic of (IR)
University of Jiroft / دانشگاه جیرفت
Iran, Islamic Republic of (IR)
How to cite
APA:
Feizabadi, A.K., Manafi, M., & Moghbeli, H. (2026). Euclidean metric frames which are not spatial. Algebra Universalis, 87(4). https://doi.org/10.1007/s00012-026-00916-z
MLA:
Feizabadi, Abolghasem Karimi, Mahmoud Manafi, and Halimeh Moghbeli. "Euclidean metric frames which are not spatial." Algebra Universalis 87.4 (2026).
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