Mathematical English Usage - a Dictionary

by Jerzy Trzeciak

include

[see also: embrace, cover, subsume, comprise, contain]

We shall only use (2), but have included (1) for completeness.

Some of the basic ideas from functional analysis are also included.

The proof is mainly included to keep the exposition as self-contained as possible.

The final lemma is due to F. Black and is included with his kind permission.

We begin by describing the class of functions $f$ considered, which includes the special cases quoted above.

This paper enlarges the class of continua with this property, namely to include those which ......

Let $Q$ denote the set of positive definite forms (including imprimitive ones, if there are any).

Let $K$ and $L$ be quasivarieties such that $K$ is properly included in $L$.

from stage $A$ up to, but not including, stage $B$



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