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Please can you explain me this notation (B)^I ,where B is basis of topology and I us interval and U belong to topology generated by B and Ui belong to (B)^I and U = union of Ui Thank you

J. W. Tanner
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Anas Echarkaoui
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  • Is it $(B)^I$ ? And $U_i$ ?. And $i\in I$ or $i\in\mathbb N$? Where is this comming from? You can you use basic Latex commands. – minorChaos Sep 11 '23 at 21:48
  • Yes from book Mathematiques Analyse cours complet avec 600 tests 'page 835 – Anas Echarkaoui Sep 11 '23 at 21:51
  • $B^I$ is the set of maps from $I$ to $B,$ i.e. the set of families $(U_i)_{i\in I}$ such that each $U_i$ is an element of $B.$ This notation is not specific to topology. – Anne Bauval Sep 11 '23 at 21:51
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    Thank you for your answer – Anas Echarkaoui Sep 11 '23 at 21:52
  • So is it solved? You are encouraged to post and accept your own answer. (I still do knot know what was meaning of the parenthesis in $(B)^I$.) – minorChaos Sep 11 '23 at 21:55
  • Imo no answer is needed: this question should be closed as a duplicate (for instance of the post linked above). This notation is not specific to topology. (Note however that in your case, the open sets of the topology generated by $B$ are the sets of the form $U=\bigcup_{i\in I}U_i,$ where $(U_i)_{i\in I}\in B^I$.) – Anne Bauval Sep 11 '23 at 22:00

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