Algebraic operations on SeparationQuotient
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In this file we define algebraic operations (multiplication, addition etc) on the separation quotient of a topological space with corresponding operation, provided that the original operation is continuous.
We also prove continuity of these operations
and show that they satisfy the same kind of laws (Monoid
etc) as the original ones.
Finally, we construct a section of the quotient map
which is a continuous linear map SeparationQuotient E →L[K] E
.
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SeparationQuotient.mk
as a MonoidHom
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SeparationQuotient.mk
as an AddMonoidHom
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Alias of SeparationQuotient.instIsUniformAddGroup
.
Alias of SeparationQuotient.instIsUniformGroup
.
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SeparationQuotient.mk
as a RingHom
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SeparationQuotient.mk
as a continuous linear map.
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The lift (as a continuous linear map) of f
with f x = f y
for Inseparable x y
.