Does Macbook AIR 13" 2013 support 4k monitors?

Question

macbook

Recently decided to update my external monitor for macbook air 13" 2013

• Processor 1.3 GHz Intel Core i5
  
• Graphics Intel HD 5000 1536 MB
  
• RAM 4 GB 1600 MHz DDR3
  

on a 4k (well, or some ± 28") monitor. Dear users, please tell me if it will work normally on my laptop at all? Does anyone have a similar experience in connecting and comfortable work? Thanks in advance for your answer!
UPD: Google in "these internets of yours" There is no exact answer.One on the Apple forum says "Yes", another "No", the third one says "Both are wrong".

Answer 1

I don’t know about 4k, but I was tormented until the beginning of November with the choice of a 24-27 "monitor for Macbook Pro 2013. I advise you to first buy an adapter (Thunderbolt-> DVI or Thunderbolt-> HDMI), with which you can already go to offline stores and check how monitors work with your macbook.
And before buying an adapter, research the topic of matching the adapter for specific displays on the Apple website.
If you are ± 28 "and you are ready to pay money for a 4k monitor (I think they are decently worth), then I advise you to look towards Apple Thunderbolt display (27").
I decided for a long time whether to buy it or not, as a result, I bought it in early November for 38k in M-video. is now in the closet.
And, if you have been determined to buy for a long time, you should hurry up - there are rumors that equipment manufacturers (Appple, Samsung) still keep prices at the "old" level so as not to lose the Russian market. So things can creep up soon.

Answer 2

Supports. But I completely agree with the speaker above.