A New Covering Dimension Function for Uniform Spaces
A New Covering Dimension Function for Uniform Spaces
复制标题
均匀空间的新覆盖维数函数
DOI：
10.1112/jlms/s2-11.2.137
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发表时间：
1975
影响因子：
1.2
通讯作者：
M. Charalambous
中科院分区：
文献类型：
--
作者：
M. Charalambous
In this paper we show that the open sets of a uniform space (X,<%) which are inverse images of open sets of R, the real numbers, under a uniformly continuous function form a perfectly normal u-frame. We are then able to introduce a dimension function<^-dim on X and apply the results of [1] to derive a very well-behaved dimension theory for uniform spaces. We have a countable sum theorem, a subset theorem, a Urysohn inequality, a product theorem and several characterisations of^-dim.<^-dim agrees with dim on Lindelof spaces and on spaces with uniformity induced by a metric. Thus the theory of 4^-dim may be considered to be an extension of the theory of covering dimension of metrisable and compact Hausdorff spaces. Tn § 3, we extend to arbitrary spaces some results previously known for Tychonoff spaces.
