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Some properties of connected spaces#1202

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phijor wants to merge 13 commits intoagda:masteragda/cubical:masterfrom

phijor:connectivity-lemmasphijor/cubical:connectivity-lemmasCopy head branch name to clipboard

Conversation Commits13 (13)Checks Files changed

Open

Some properties of connected spaces#1202
phijor wants to merge 13 commits intoagda:masterfrom
phijor:connectivity-lemmas

Commits

Commits on May 19, 2025

Being n-connected is a proposition
phijor
committed
Being an n-connected function is a proposition
phijor
committed
A type is n-connected iff every map to an n-type is constant
phijor
committed
All k-connected k-types are are contractible
phijor
committed
A type is (k+1)-connected iff it is merely inhabited and has k-connected paths
phijor
committed
A type is (k+1)-connected iff it is (k+1)-inhabited and has k-connected paths
phijor
committed
All loop spaces of a (k+2)-connected type are merely equivalent
phijor
committed
Avoid univalence in proof of `isConnectedFun→isConnected` and converse
phijor
committed
Restructure proof of `indMapEquiv→conType`
phijor
committed
Strengthen `indMapEquiv→conType` to only require existence of a section
phijor
committed
A pointed type is connected iff all points merely have a path to the base
phijor
committed
Promote some isomorphisms of truncations to equivalences
phijor
committed
Connected types are closed under `Σ`
phijor
committed

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