Neighborhood spaces

Article English OPEN
Kent, D. C. ; Min, Won Keun (2002)
  • Publisher: Hindawi Publishing Corporation
  • Journal: International Journal of Mathematics and Mathematical Sciences (issn: 0161-1712, eissn: 1687-0425)
  • Related identifiers: doi: 10.1155/S0161171202202203
  • Subject: Mathematics | QA1-939
    arxiv: Mathematics::Category Theory

Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and bicoreflectively embedded in CLS. Initial and final structures are described in these categories, and it is shown that the Tychonov theorem holds in all of them. In order to describe a successful convergence theory in NBD, it is necessary to replace filters by more general p-stacks.
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