I have a polygon representing a wall.
Is there a topology check on ArcGIS Desktop to close gaps like this? Or is there a different workflow I can try?
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You could also try tool Integrate:
Integrate is used to maintain the integrity of shared feature boundaries by making features coincident if they fall within the specified x,y tolerance. Features that fall within the specified x,y tolerance are considered identical or coincident.
The tool will modify your data so be sure to backup before executing.
Two idea come to mind:
2) Buffer and negative buffer.
Buffer the polygons by X distance followed by buffering the buffered polygons by -X distance. Make sure to select the dissolve polygons option.
One potentially bad consequence to be aware of with this option is that corners may be rounded the greater the buffer distance.