Documentation
PiBaseLean
.
Properties
.
P63
.
Defs
Search
return to top
source
Imports
Init
Mathlib.Topology.Separation.CompletelyRegular
Imported by
PiBase
.
CechCompleteSpace
source
class
PiBase
.
CechCompleteSpace
(
X
:
Type
u)
[
TopologicalSpace
X
]
extends
T35Space
X
:
Prop
t0
⦃
x
y
:
X
⦄
:
Inseparable
x
y
→
x
=
y
completely_regular
(
x
:
X
)
(
K
:
Set
X
)
:
IsClosed
K
→
x
∉
K
→
∃ (
f
:
X
→
↑
unitInterval
),
Continuous
f
∧
f
x
=
0
∧
Set.EqOn
f
1
K
is_gδ :
IsGδ
(
Set.range
stoneCechUnit
)
Instances