TY - JOUR
AU - Di Maio, Giuseppe
AU - Meccariello, Enrico
AU - Naimpally, Somashekhar
PY - 2006/10/01
Y2 - 2024/06/17
TI - Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 7
IS - 2
SE -
DO - 10.4995/agt.2006.1927
UR - https://polipapers.upv.es/index.php/AGT/article/view/1927
SP - 245-252
AB - <p>Recently it was shown that the lower Hausdorff metric (uniform) topology is generated by families of uniformly discrete sets as hit sets. This result leads to a new hypertopology which is the join of the above topology and the upper Vietoris topology. This uniformly discrete hit-and-miss hypertopology is coarser than the locally finite hypertopology and finer than both Hausdorff metric (uniform) topology and Vietoris topology. In this paper this new hypertopology is studied. Here is a Hasse diagram in which each arrow goes from a coarser topology to a finer one and equality follows UC or TB as indicated. The diagram clearly shows that the new (underlined) topology provides the missing link.</p>
ER -