Uniqueness Conditions of the Representation of a Topology in Top(X)
In this article motivated by unique representation of a topology τ on X , we introduce some kind of representation for τ in T o p ( X ) and find the equivalent condition for a topological space to have unique representation. As the main part of the paper, we introduce the natural representation for...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2018-10, Vol.41 (4), p.1953-1967 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this article motivated by unique representation of a topology
τ
on
X
, we introduce some kind of representation for
τ
in
T
o
p
(
X
)
and find the equivalent condition for a topological space to have unique representation. As the main part of the paper, we introduce the natural representation for every topology
τ
on a set
X
of the form
⋀
a
∈
L
(
X
)
T
(
a
,
W
a
)
, where
W
a
is the set of all neighborhoods and deleted neighborhoods of
a
and
L
(
X
) is the set of all non-isolated points of
X
, and we characterize the spaces whose topology has unique representation. Also it is proved that every first countable Hausdorff space has unique representation property. |
|---|---|
| ISSN: | 0126-6705 2180-4206 |
| DOI: | 10.1007/s40840-016-0436-x |