Showing that a given set is a basis for X x Y.

**thedoctor818** · September 7th 2010, 04:01 PM

Show that if $\mathcal{B}$ is a basis for $X$ and $\mathcal{G}$ is a basis for $Y$ , then $\mathcal{B} \times \mathcal{G} = \{B \times G|B \in \mathcal{B}, G \in \mathcal{G}\}$ is a basis for $X \times Y.$

Any help would be appreciated.

**Plato** · September 7th 2010, 04:32 PM

This question is too vague to answer.
The basis for what?
Are we in a vector space, a metric space, or a general topological space?
You must be very specific in asking a question. We are not mind-reader.

**thedoctor818** · September 7th 2010, 04:37 PM

Sorry, we are in a general topological space.

**Plato** · September 7th 2010, 04:54 PM

Well O.K.
What defines a basis?
Does $\mathcal{B} \times \mathcal{G}$ constitute a basis?

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