Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/8273
Title: A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes
Authors: Dimov, Georgi D.
Keywords: Euclidean spacesTychonoff cubesspherestori(locally) compact Hausdorff spacesdualityregular closed setssums of local contact algebrassums of normal contact algebras
Issue Date: 2012
Publisher: EUT Edizioni Università di Trieste
Source: Georgi D. Dimov, "A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 44 (2012), pp. 45–74.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
44 (2012)
Abstract: 
In the beginning of the 20th century, A. N. White-
head [39, 40] and T. de Laguna [9] proposed a new theory of space,
known as region-based theory of space. They did not present their ideas
in a detailed mathematical form. In 1997, P. Roeper [33] has shown
that the locally compact Hausdorff spaces correspond bijectively (up to
homeomorphism and isomorphism) to some algebraical objects which
represent correctly Whitehead’s ideas of region and contact relation,
generalizing in this way a previous analogous result of de Vries [10] con-
cerning compact Hausdorff spaces (note that even a duality for the cate-
gory of compact Hausdorff spaces and continuous maps was constructed
by de Vries [10]). Recently, a duality for the category of locally compact
Hausdorff spaces and continuous maps, based on Roeper’s results, was
obtained in [11] (it extends de Vries’ duality mentioned above). In this
paper, using the dualities obtained in [10, 11], we construct directly (i.e.
without the help of the corresponding topological spaces) the dual objects
of Euclidean spaces, spheres, tori and Tychonoff cubes; these algebraical
objects completely characterize the mentioned topological spaces. Thus,
a mathematical realization of the original philosophical ideas of White-
head [39, 40] and de Laguna [9] about Euclidean spaces is obtained.
Type: Article
URI: http://hdl.handle.net/10077/8273
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.44 (2012)

Files in This Item:
File Description SizeFormat
Dimov_RIMUT44.pdf357.5 kBAdobe PDFThumbnail
View/Open
Show full item record

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.



CORE Recommender

Page view(s) 50

724
checked on Apr 1, 2020

Download(s) 50

482
checked on Apr 1, 2020

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.