TY - JOUR
ID - 32712
TI - On the pointfree counterpart of the local definition of classical continuous maps
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Banaschewski, Bernhard
AD - Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.
Y1 - 2018
PY - 2018
VL - 8
IS - 1
SP - 1
EP - 8
KW - Pointfree topology
KW - continuous map
KW - localic maps
DO - 10.29252/cgasa.8.1.1
N2 - 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 [4]). This note presents alternative proofs of these pointfree results which differ from those of [4] 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.
UR - https://cgasa.sbu.ac.ir/article_32712.html
L1 - https://cgasa.sbu.ac.ir/article_32712_7102051b8b0d2b0555b4ab6cee021fc7.pdf
ER -