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Hard to say from just the pics but almost certainly it's a gel rollerball pen with a very fine nib, probably ~0.5mm. Looks very much like a Pilot G1 to me.
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/43805 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/43805 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/