Algebraic topology Homotopy: basic notions Concept
Pointed space
Summary
A pointed space is a topological space together with a chosen point, its base point. Maps of pointed spaces are continuous maps that send base point to base point. Many constructions of homotopy theory need a base point, such as the fundamental group, the loop space and the wedge sum.
Where this leads
18 pages build on this one.
- Homotopy fiber
- Eckmann–Hilton duality
- Stable homotopy theory
- Freudenthal suspension theorem
- Sullivan conjecture
- Infinite loop space
- H-space
- Symmetric spectrum
- Wedge sum
- Puppe sequence
- Homotopy group with coefficients
- Loop space
- Fundamental group
- Homotopy group
- Path space fibration
- Toda bracket
- Whitehead product
- Spectrum
Further reading
About this page
| Tag | T9DG8DDE75 |
|---|---|
| URI | m2://T9DG8DDE75 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 55P99, 55Q05 |
| Specializes | Topological space |
| Same as | |
| Changed | 2 November 2026 |
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What links here
Used by
- Homotopy fiber
- Eckmann–Hilton duality
- Stable homotopy theory
- Freudenthal suspension theorem
- Sullivan conjecture
- Infinite loop space
- H-space
- Symmetric spectrum
- Wedge sum
- Puppe sequence
- Homotopy group with coefficients
- Loop space
- Fundamental group
- Homotopy group
- Path space fibration
- Toda bracket
- Whitehead product
- Spectrum