%0 Journal Article %T On the pointfree counterpart of the local definition of classical continuous maps %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Banaschewski, Bernhard %D 2018 %\ 01/01/2018 %V 8 %N 1 %P 1-8 %! On the pointfree counterpart of the local definition of classical continuous maps %K Pointfree topology %K continuous map %K localic maps %R 10.29252/cgasa.8.1.1 %X 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. %U https://cgasa.sbu.ac.ir/article_32712_7102051b8b0d2b0555b4ab6cee021fc7.pdf