Database
BASIC TOPOLOGY
Topology
Topological spaces
Topologies
0ntop
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topopn
Metamath Proof Explorer
Ascii
Structured
Theorem
0ntop
Description:
The empty set is not a topology.
(Contributed by
FL
, 1-Jun-2008)
Ref
Expression
Assertion
0ntop
⊢
¬ ∅ ∈ Top
Proof
Step
Hyp
Ref
Expression
1
noel
⊢
¬ ∅ ∈ ∅
2
0opn
⊢
( ∅ ∈ Top → ∅ ∈ ∅ )
3
1
2
mto
⊢
¬ ∅ ∈ Top