Di Maio, G.; Meccariello, E.; Naimpally, S. (2006). Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies. Applied General Topology. 7(2):245-252. doi:10.4995/agt.2006.1927.
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/83048
Title:
|
Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies
|
Author:
|
Di Maio, Giuseppe
Meccariello, Enrico
Naimpally, Somashekhar
|
Issued date:
|
|
Abstract:
|
[EN] 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 ...[+]
[EN] 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.
[-]
|
Subjects:
|
Hypertopology
,
Hausdorff metric
,
Vietoris topology
,
Proximal topology
,
Proximal locally finite
,
Hit-and-miss hypertopology
,
ε-discrete subset
,
Uniformly discrete
,
Uniformly isolated
,
locally finite family
|
Copyrigths:
|
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
|
Source:
|
Applied General Topology. (issn:
1576-9402
) (eissn:
1989-4147
)
|
DOI:
|
10.4995/agt.2006.1927
|
Publisher:
|
Universitat Politècnica de València
|
Publisher version:
|
https://doi.org/10.4995/agt.2006.1927
|
Type:
|
Artículo
|