Sorry, no online dictionaries contain the exact phrase closeness function.
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Reverse dictionary results:
1. density
 2. degree
3. intimacy
4. intimate
5. juxtaposition
6. neighborhood
7. parsimony
8. pith
9. presence
10. propinquity
 11. proximity
12. friendship
13. meanness
14. caress
15. grit
16. grits
17. intention
18. similarity
19. account
20. adjunct
 21. analogue
22. analysis
23. audit
24. band
25. break
26. burnout
27. closure
28. collapse
29. convergence
30. correspond
 31. correspondence
32. damage
33. degrade
34. depression
35. down
36. effective
37. equivalence
38. even
39. exercise
40. exercising

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You can look up the words in the phrase individually using these links:   closeness ?   function ?
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Not helpful? You might try using the wildcards * and ? to find the word you're looking for. For example, use
clos*to search for words beginning with clos, or
*tionto search for words ending with tion
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