Can someone please describe the standard topology on the closed interval [0,1]? It seems (to me) like it should consist of the open balls, {0}, and {1} (and the union/finite intersection of these, etc.)... Thanks.
Can someone please describe the standard topology on the closed interval [0,1]? It seems (to me) like it should consist of the open balls, {0}, and {1} (and the union/finite intersection of these, etc.)... Thanks.
I assume you mean a subset topology.
Since is a subset of it means is open iff for some open subset of .
Therefore, the open sets of under the subspace topology are , , where .
Can someone please describe the standard topology on the closed interval [0,1]? It seems (to me) like it should consist of the open balls, {0}, and {1} (and the union/finite intersection of these, etc.)... Thanks.
You don't talk about balls in this dimension oO
The standard topology of [0,1] may be the subspace topology on