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- Title
Alexandroff Spaces.
- Authors
Rose, David; Scible, Gregg; Walsh, Danielle
- Abstract
We show first that every topology τ has a minimum Alexandroff topology expansion τA and investigate such expansion topologies. Then we lift the Ginsburg structure theorem for homogeneous finite spaces to the class of homogeneous partition spaces which includes the class of homogeneous locally finite spaces. Finally, we introduce the class of upper bounded (lower bounded) T0 Alexandroff spaces which properly contains the class of Artinian (Noetherian) T0 Alexandroff spaces and prove that a T0 Alexandroff space is compact if and only if it is both lower bounded and has a finite set of minimal elements in the specialization order.
- Subjects
TOPOLOGY; COMPACT spaces (Topology); INTERSECTION theory; MONOTONIC functions; IDEMPOTENTS
- Publication
Journal of Advanced Studies in Topology, 2012, Vol 3, Issue 1, p31
- ISSN
2090-388X
- Publication type
Article
- DOI
10.20454/jast.2012.233