The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
Homological algebra with locally compact abelian groups , Url =
3 Pith papers cite this work. Polarity classification is still indexing.
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Introduces the group E^ws_TA(A,B) of weakly split extensions in topological Abelian groups, gives descriptions as continuous sum structures on B×A and as a cocycle quotient Z_c/B_c, relates it to ordinary extensions via a six-term exact sequence, and supplies examples for discrete groups with Bohr t
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
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Weak split extensions of topological Abelian groups
Introduces the group E^ws_TA(A,B) of weakly split extensions in topological Abelian groups, gives descriptions as continuous sum structures on B×A and as a cocycle quotient Z_c/B_c, relates it to ordinary extensions via a six-term exact sequence, and supplies examples for discrete groups with Bohr t
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Shape theory for condensed anima
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.