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Imports
Init
LeanCourse.Common
Mathlib.Topology.Instances.Real
Imported by
principal
Tendsto₁
Tendsto₂
source
def
principal
{α :
Type
u_1}
(s :
Set
α
)
:
Filter
α
Equations
principal
s
=
{
sets
:=
{
t
:
Set
α
|
s
⊆
t
}
,
univ_sets
:=
⋯
,
sets_of_superset
:=
⋯
,
inter_sets
:=
⋯
}
Instances For
source
def
Tendsto₁
{X :
Type
u_1}
{Y :
Type
u_2}
(f :
X
→
Y
)
(F :
Filter
X
)
(G :
Filter
Y
)
:
Prop
Equations
Tendsto₁
f
F
G
=
∀
V
∈
G
,
f
⁻¹'
V
∈
F
Instances For
source
def
Tendsto₂
{X :
Type
u_1}
{Y :
Type
u_2}
(f :
X
→
Y
)
(F :
Filter
X
)
(G :
Filter
Y
)
:
Prop
Equations
Tendsto₂
f
F
G
=
(
Filter.map
f
F
≤
G
)
Instances For