How do I merge these two objects in Inkscape such that the space in between is gone?

To make a united object we may select Path > Union Ctrl+ after we had selected the objects we wanted to unite.

Gaps between objects will remain visible in the united objects. Therefore we have to remove any gaps before we proceed.

This can be done in several ways, depending on the precision we need for the objects or their surroundings:

1. Move objects until they overlap
   By this the original position of the object will change of course

2. Move object handles until they snap to the neighboring object’s handle

   • in path mode enable snapping to handles or corners.
   • Drag neighboring handles until they “snap”:

   

   • Make a union object Ctrl+.

3. Create a third object filling the gap (this object can be larger than the gap):

   • It is easier to create such an object when snapping is enabled.

   

   • Select all three objects to create a unified object Ctrl+