To tile/repeat an image in the material using the UV editor, you would need to scale up the UV map and place it manually on the image (the UV map will need to be larger than the bounds of the image). The tiling/repeated-image used as texture will be visible on the 3d viewport in material preview mode or in render preview mode.
To view the tiled the image in the UV editor. Press N to show the editor properties and in the view tab enable Repeat Image.
Old Answer (I'll keep it just to reference the comments)
Use a texture coordinate node to set the texture to use UV coordinates.
With a mapping node you can control the location rotation and scale of the texture used.
Changing the scale will allow you to repeat the texture within the UV coordinates.
Note that when you use Pont as the type, a scale of 5 means that the texture will be repeated 5 times on a given axis.
Also note that the image texture node has to be set to Repeat.
If you choose Texture as Type on the mapping node then you can repeat the texture by using values smaller than 1.0, for example a value of 0.2 will repeat the image texture 5 times.
The texture can be visualized in the Preview window for the material