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fixing some docs
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zstone1 committed Oct 26, 2024
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Showing 1 changed file with 13 additions and 7 deletions.
20 changes: 13 additions & 7 deletions theories/topology_theory/subtype_topology.v
Original file line number Diff line number Diff line change
Expand Up @@ -7,16 +7,22 @@ From mathcomp Require Import product_topology subspace_topology.
(**md**************************************************************************)
(* # Subtypes of topological spaces *)
(* We have two distinct ways of building topologies as subsets of a *)
(* topological space `X`. One is the `subspace topology`, which builds a new *)
(* topology on X which 'isolates' a set A. The other considers the sigma *)
(* type `set_type` in the weak topology by the inclusion. Note `subspace A` *)
(* has the advantage that it preserves all the algebraic structure on X, and *)
(* the relevant local behavior A (in particular, continuity). On the other *)
(* hand `set_val A` has the right global properties you'd expect for the *)
(* subset topology. But you can't easily add two elements of `set_val [0,1]`. *)
(* topological space `X`. One is the `subspace topology`, which is defined in *)
(* `subspace_topology.v`. It builds a topology on X which 'isolates' a set A. *)
(* Ther other, defined in this file, defines a topology on the sigma type *)
(* `set_type` in the weak topology by the inclusion. Note `subspace A` has *)
(* the advantage that it preserves all the algebraic structure on X, but only *)
(* the local behavior A (in particular, continuity). On the other hand *)
(* `set_type A` has the right global properties you'd expect for the subset *)
(* topology. But you can't easily add two elements of `set_val [0,1]`. *)
(* Note the implicit coercion from sets to `set_val` from `classical`. *)
(* *)
(* This file provides `set_type` with a topology, and some theory. *)
(* ``` *)
(* sigT_of_setX == commutes `set_type` and product topologies *)
(* setX_of_sigT == commutes product and `set_type` topologies *)
(* ``` *)
(* *)
(******************************************************************************)

Local Open Scope classical_set_scope.
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