How to extend an existing font and create a new glyph for space (U0020)

I'm trying to extend a font and modify the space character. My aim is serve a customized font face to substitute white spaces with a mid point. (e.g U00b7).

For this specific example I used CenturyGothic and with FontForge modified the space glyph to something similar to mid point.

As expected, all spaces are showing the modified glyph, however, zero width spaces and other type of spaces are also showing the same glyph. I suspect there is some linkage going on ? Never worked with font forge before.

How would I go on about to show the modified glyph explicitly for spaces (U0020)?

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