Category:Product Spaces

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This category contains results about Product Spaces in the context of Topology.


Let $\struct{S_1, \tau_1}$ and $\struct{S_2, \tau_2}$ be topological spaces.

Let $S_1 \times S_2$ be the cartesian product of $S_1$ and $S_2$.

Let $\tau$ be the Tychonoff topology on $S_1 \times S_2$.

From Natural Basis of Tychonoff Topology of Finite Product, $\tau$ is the topology generated by the basis

$\BB = \set{U_1 \times U_2: U_1 \in \tau_1, U_2 \in \tau_2}$.


The topological space $\struct{S_1 \times S_2, \tau}$ is called the product space of $\struct{S_1, \tau_1}$ and $\struct{S_2, \tau_2}$.

Subcategories

This category has only the following subcategory.

Pages in category "Product Spaces"

The following 54 pages are in this category, out of 54 total.