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Spaces of functions and sections with paracompact domain
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 21 November 2023, pp. 1-23
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- Article
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We study spaces of continuous functions and sections with domain a paracompact Hausdorff k-space $X$
and range a nilpotent CW complex $Y$
, with emphasis on localization at a set of primes. For $\mathop {\rm map}\nolimits _\phi (X,\,Y)$
, the space of maps with prescribed restriction $\phi$
on a suitable subspace $A\subset X$
, we construct a natural spectral sequence of groups that converges to $\pi _*(\mathop {\rm map}\nolimits _\phi (X,\,Y))$
and allows for detection of localization on the level of $E^2$
. Our applications extend and unify the previously known results.
