On the pointfree counterpart of the local definition of classical continuous maps
Publish Year: 1397
نوع سند: مقاله ژورنالی
زبان: English
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JR_CGASAT-8-1_001
تاریخ نمایه سازی: 23 شهریور 1400
Abstract:
The familiar classical result that a continuous map from a space X to a space Y can be defined by giving continuous maps \varphi_U: U \to Y on each member U of an open cover {\mathfrak C} of X such that \varphi_U\mid U \cap V = \varphi_V \mid U \cap V for all U,V \in {\mathfrak C} was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar classical counterpart concerning finite closed covers of a space X (Picado and Pultr [۴]). This note presents alternative proofs of these pointfree results which differ from those of [۴] by treating the issue in terms of frame homomorphisms while the latter deals with the dual situation concerning localic maps. A notable advantage of the present approach is that it also provides proofs of the analogous results for some significant variants of frames which are not covered by the localic arguments.
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Authors
Bernhard Banaschewski
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L۸S ۴K۱, Canada.
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