- #1
V0ODO0CH1LD
- 278
- 0
The topology ## T ## on a set ## X ## generated by a basis ## B ## is defined as:
[tex] T=\{U\subset X:\forall\ x\in U\ there\ is\ a\ \beta\in B:x\in \beta \ and\ \beta\subset U \}. [/tex]
But if ##U## is the empty set, and there has to be a ## \beta ## in ##B## that is contained in ##U##, the empty set has to be in ## B ## because only the empty set contains the empty set. Right?
If there is something I am missing, how is the empty set part of the topology generated by a basis?
[tex] T=\{U\subset X:\forall\ x\in U\ there\ is\ a\ \beta\in B:x\in \beta \ and\ \beta\subset U \}. [/tex]
But if ##U## is the empty set, and there has to be a ## \beta ## in ##B## that is contained in ##U##, the empty set has to be in ## B ## because only the empty set contains the empty set. Right?
If there is something I am missing, how is the empty set part of the topology generated by a basis?