open interval

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A set of numbers consisting of all the numbers between a pair of given numbers but not including the endpoints.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun mathematics an interval in the real number line which does not contain its supremum and infimum. If specified by a pair of real numbers, then it consists of all the points on the real line whose values lie strictly between those two real numbers.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun an interval that does not include its endpoints