Abstract: “In this paper we have to studied about a closed linear space of dual nuclear beally conver space, we have to considered that quotient spaces of dual nuclear locally convex space, by itself closed linear space, we have to proved that this quotient space is also dual nuclear. We have also studied about a given canonical mapping from one canonical bounded space to another bounded space. We have prove that the locally convexspace in this connection is dual nuclear. Finally we have discussed about the given canonical mapping from one pre-compact canonical sub space into another pre-compact canonical sub space. We have shown that the concerning locally convex space is dual nuclear. Canonical Mapping may also be applied in visualizing Dynamic data with maps for this purpose we have:-Creating maps from Graph Data. Maps of Dynamic Data Maps of Readability.”

Keywords: convex space, bounded set, linear space, dual nuclear, close linear space