Usually means: Includes start, excludes end point.
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We found 5 dictionaries that define the word half-open:

General (5 matching dictionaries)
  1. half-open: Merriam-Webster
  2. half-open, half-open: Collins English Dictionary
  3. Half-open, half-open: Wordnik
  4. half-open: Wiktionary
  5. half-open: TheFreeDictionary.com

Definitions from Wiktionary (half-open)

adjective:  partially open; ajar
adjective:  (mathematics) (referring to an interval on the real line) containing only one of its endpoints

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