A note on the core topology and three other ones
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2005
scientific article
english
- topology
- real linear space
EN In the paper there are considered the topologies defined in real linear spaces: the core topology, the topology generated by the family of directionally continuous functions, and the topology defined by Klee in [7]. The notion of the last one is extended to infinite dimensional case by means of the finite topology investigated by Kakutani and Klee [5]. Some properties of the finite topology are proved. The main result says that every one of considered topologies contain essentially the next one in the order listed above.
49 - 63
CC BY-NC-ND (attribution - noncommercial - no derivatives)
public