TOPOLOGY WITHOUT POINTS
作者:
ArnoldA. Johanson,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1981)
卷期:
Volume 4,
issue 3
页码: 185-200
ISSN:1607-3606
年代: 1981
DOI:10.1080/16073606.1981.9631871
出版商: Taylor & Francis Group
关键词: 54A99;06E15;18F99;54E17
数据来源: Taylor
摘要:
Other theories that develop topology without points are either excessively artificial or suffer from a lack of rigor. In this paper it is assumed that worlds W are composed of parts that form a complete Boolean algebra [xbar] and that the collection [Wbar] of all points of W is a certain subcollection of all filters defined over [xbar]. Two axioms are given for points which, given suitable definitions, convert [Wbar] into a compact Hausdorff space. Nearness collections of parts of W are defined which satisfy all the axioms of Herrlich for nearness except that closure is defined without mentioning points and consequently one may define closed and open parts. A category of worlds is defined in which the objects are lattices of closed parts of a world and the arrows are roughly speaking the far-preserving mps. It is shown that the category of compact T1-spaces is a reflective subcategory of the category of worlds.
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