Typesetters in Europe eventually agreed to use one space sometime near the early 20th century, with American typesetters following suit shortly thereafter, according to James Felici, author of The Complete Manual of Typography.
For the Love of God, Stop Putting Two Spaces After a Period
John McDermott
317145

One source? A quick search on the internet points to a different time frame for the disappearance of the extra space. More likely the late 50’s to early 60’s.

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