Sorry, no online dictionaries contain the exact phrase finite paracompact.
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Reverse dictionary results:
1. ended
2. limited
3. bounded
4. end
5. finitely
6. finiteness
7. finitude
8. infinite
9. real
10. accusative
11. adn
12. affine
13. algebraic
14. algebraical
15. algorithm
16. algorithmic
17. alphabet
18. amd
19. and
20. ane
21. ans
22. automaton
23. bernoulli distribution
24. binomial distribution
25. boundedness
26. certain
27. character
28. clause
29. combinatorics
30. compact
31. compactification
32. configuration
33. converge
34. convergence
35. convergency
36. convergent
37. curve
38. cycle
39. delta
40. dfa

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You can look up the words in the phrase individually using these links:   finite ?   paracompact ?
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