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Epireflective subcategories of TOP, T2UNIF, UNIF, closed under epimorphic images, or being algebraic
The epireflective subcategories of Top , that are closed under epimorphic (or bimorphic) images, are { X ∣ | X | ≤ 1 } , { X ∣ X is indiscrete } and Top . The epireflective subcategories of T 2 Unif , closed under epimorphic images, are: { X ∣ | X | ≤ 1 } , { X ∣ X is compact T 2 } , { X ∣ covering...
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| Published in: | Periodica mathematica Hungarica 2016-06, Vol.72 (2), p.112-129 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The epireflective subcategories of
Top
, that are closed under epimorphic (or bimorphic) images, are
{
X
∣
|
X
|
≤
1
}
,
{
X
∣
X
is indiscrete
}
and
Top
. The epireflective subcategories of
T
2
Unif
, closed under epimorphic images, are:
{
X
∣
|
X
|
≤
1
}
,
{
X
∣
X
is compact
T
2
}
,
{
X
∣
covering character of
X
is
≤
λ
0
}
(where
λ
0
is an infinite cardinal), and
T
2
Unif
. The epireflective subcategories of
Unif
, closed under epimorphic (or bimorphic) images, are:
{
X
∣
|
X
|
≤
1
}
,
{
X
∣
X
is indiscrete
}
,
{
X
∣
covering character of
X
is
≤
λ
0
}
(where
λ
0
is an infinite cardinal), and
Unif
. The epireflective subcategories of
Top
, that are algebraic categories, are
{
X
∣
|
X
|
≤
1
}
, and
{
X
∣
X
is indiscrete
}
. The subcategories of
Unif
, closed under products and closed subspaces and being varietal, are
{
X
∣
|
X
|
≤
1
}
,
{
X
∣
X
is indiscrete
}
,
{
X
∣
X
is compact
T
2
}
. The subcategories of
Unif
, closed under products and closed subspaces and being algebraic, are
{
X
∣
X
is indiscrete
}
, and all epireflective subcategories of
{
X
∣
X
is compact
T
2
}
. Also we give a sharpened form of a theorem of Kannan-Soundararajan about classes of
T
3
spaces, closed for products, closed subspaces and surjective images. |
|---|---|
| ISSN: | 0031-5303 1588-2829 |
| DOI: | 10.1007/s10998-016-0110-y |