[see also: call, designate, write, set, symbol, label, relabel, rename
Denote by P the space of...... [Not: “Note P the space of......'']
We let T denote the set of......
......with e0 denoting multiplication by f.
The wedge denotes that ei has been omitted.
Then we can find a subsequence (still denoted by an) such that an<1 for all n.
[Rather than: “Denote f=......”, write: Define <Set/Let/Write> f=......]