Definition:Product Topology/Also known as
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Product Topology: Also known as
The product topology is also known as the Tychonoff topology, named for Andrey Nikolayevich Tychonoff.
While both of these terms are commonly used on $\mathsf{Pr} \infty \mathsf{fWiki}$, the preference is for product topology.
Various other terms can be found in the literature for the product space, for example:
- direct product
- topological product
- Tychonoff product
but these terms are less precise, and there exists the danger of confusion with other similar uses of these terms in different contexts.
Note that the topological space $\struct {\XX, \tau}$ itself is never referred to as a Tychonoff space.
This is because a Tychonoff space is a different concept altogether.