LG 25UN58 full resolution please on a mini Mac mid 2011

Open the Displays Preference, hold the Alt (option) key and click on the Scaled button.

Then see if you can select the resolution that you are looking for...?

If not, then try a different Mini DisplayPort to HDMI adapter or a Display that offers either DVI or Display Port inputs.

If it is displaying 1080p and the screen is filled out than you ARE getting 2560x1080. Any less than 2560 and your screen would be out of proportion. This TV's max HDMI is 1920x1080 but the Display prefs show 1080p in scaled which is also the default resolution'

I'm beginning to think that your monitor as the prompt says is not supported by Mac since it only has an HDMI connection. If you go to Display Prefs can you get the resolution to say 2560x1080 or does it show 1080p for both default and scaled? Possibly this might help some but I'm not sure.

When you have the monitor connected, does it fill the whole screen? Also, does it look correct in that objects are not distorted and text crisp? If so possibly the mini is only recognizing the height of the monitor not necessarily the width.

You could try SwitchResX and see if you could put in the resolution that you are seeking.

I believe that this is simply a matter of not understanding what the default resolution showing (1080P) is.

2560 x 1080 IS 1080P (HD). You won't be able to get a better resolution, because a height of 1080 is the highest resolution of your monitor.

The computer cannot show a resolution that the monitor is not capable of achieving. Your monitor can only display at 1080 regardless of the capability of the computer. You will only be able to get 2560x1080, the monitor's max or native display rate. To achieve the max capable by the computer you will need a monitor that is capable of that resolution. I have a HP 34C Envy which is capable of 3840x2160 but with my Late 2012 mini I can only get 2560x1440.

My regular monitor is a 50" LCD flat screen UHD but I can only get 1920x1080. With an Active Mini Display Port to HDMI adapter I can get 3840x2160. The main caveats are the refresh rate(30herz) is too slow for gaming and the system fonts in the menu bar are just too small and non adjustable.

The person in the Apple Store told you correctly that the Thunderbolt to HDMI adapter would work which by your own admission does. The 1080 aspect is part of the monitor's native resolution. As per my other post the computer cannot force the monitor to display a resolution it cannot attain. When you go into scaled in the display prefs you will see the resolutions are all smaller than than the native resolution of 2560x1080. There is nothing you can do or buy that will change it. If you want a higher resolution than you will have to get a monitor capable of it.

What do you plan on doing? There is no adapter that will enable you to achieve the max resolution of your mini on that monitor. 2560x1080 is max regardless of what the mini is capable of displaying.

Not to belabor this point, if the Apple store is nearby make an appointment and take your monitor and Thunderbolt to HDMI adapter and have them hook up to a newer Mac mini(they are capable of 4K) and see if they can get anything higher than what you get. I'll guarantee that it will be the same.

I was the one that told you about the Active adapter. I really did not think that it would work on a lower resolution but glad you gave it a try and it worked. Kind of like a Christmas gift unknowingly. Enjoy your monitor and if you have other problems you eventually can find the solution here on Apple Discussions.

By the monitor specs you are limited to 2560x1080