The man lives close to the market.
Here the word 'close' is a/an -

• Close শব্দটি বিভিন্ন Parts of Speech হিসেবে ব্যবহৃত হয়। 

• Close (noun): 
Meaning - The end of something, or the time when you end it. 
Example - The season is now nearing its close.

• Close (adjective): 
Meaning - Having direct family connections or shared beliefs, support, and sympathy.
Example - There weren't many people at the funeral - just close family/relatives.

• Close (verb): 
Meaning - To change from being open to not being open, or to cause something to do this; বন্ধ করা; বন্ধ হওয়া।
Example - I went out and forgot to close the window.

• Close (adverb): 
Meaning - Near in position, time, or condition: ঘনিষ্ঠভাবে; আবদ্ধভাবে; দৃঢ়ভাবে; কাছাকাছি।
Example - The bank is close to the office.

⇒ The man lives close to the market.
- এই sentence টিতে 'close' শব্দটি lives (verb)- কে modify করছে। 
- Adverb সাধারণত verb, adjective অথবা অন্য adverb কে modify করে। 
- তাই এখানে 'close' হচ্ছে Adverb. 

Source: 
1. Cambridge Dictionary. 
2. Accessible Dictionary by Bangla Academy.