instTopologicalSpaceObjOppositeCompHausValOpOfPUnit

English

For a condensed set X, the topology on the carrier X(*) is defined as the coinduced topology from the coinducingCoprod map, i.e., the coinduced topology along the coprojection from test objects.

Русский

Для конденсированного множества X топология на X(*) определяется как сочиненная по конийной топологии через карту coinducingCoprod.

LaTeX

$$$\text{TopologicalSpace}(X^{*}) = \mathrm{TopologicalSpace.coinduced}(\mathrm{coinducingCoprod\,X})$$$

Lean4

/-- Let `X` be a condensed set. We define a topology on `X(*)` as the quotient topology of
all the maps from compact Hausdorff `S` spaces to `X(*)`, corresponding to elements of `X(S)`.
In other words, the topology coinduced by the map `CondensedSet.coinducingCoprod` above. -/
local instance : TopologicalSpace (X.val.obj ⟨CompHaus.of PUnit⟩) :=
  TopologicalSpace.coinduced (coinducingCoprod X) inferInstance

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