General topology Constructions of spaces Concept
Product topology
Summary
The product topology is the natural topology on a Cartesian product of topological spaces. It is the coarsest topology for which all projections onto the factors are continuous.
Where this leads
34 pages build on this one.
- Homotopy
- Suspension
- Profinite completion
- Brouwer's characterization of the Cantor space
- Sorgenfrey plane
- Homotopy fiber
- Determinacy
- Analytic set
- Stable homotopy theory
- Cantor group
- Continuous multiplication
- Topological vector space
- Shift space
- Projective determinacy
- Tychonoff plank
- Topology of pointwise convergence
- FK-space
- Thom spectrum
- Local trivialization
- Topological transformation group
- Whitney sum
- Projective hierarchy
- Adele ring
- Baire space of sequences
- Join
- Toda bracket
- Mapping cylinder
- Cantor algebra
- Tube lemma
- Cantor space
- Axiom of determinacy
- Algorithmic randomness
- Associated bundle
- Spectrum
Further reading
- Web https://en.wikipedia.org/wiki/Product_topology, lead section
About this page
| Tag | 0GBG8B49AA |
|---|---|
| URI | m2://0GBG8B49AA |
| Aliases | tychonoff-topology |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54B10 |
| Same as |
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What this page needs for W2
- edge equivalent in: a statement for each pair of definitions that a source proves equivalent (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Homotopy
- Suspension
- Profinite completion
- Sorgenfrey plane
- Homotopy fiber
- Cantor group
- Continuous multiplication
- Topological vector space
- Shift space
- Tychonoff plank
- Topology of pointwise convergence
- FK-space
- Local trivialization
- Topological transformation group
- Whitney sum
- Adele ring
- Baire space of sequences
- Join
- Mapping cylinder
- Tube lemma
- Cantor space
- Associated bundle