| Clue | Answer |
| A topological space is compact if every open cover has a(n) _____________ | |
| An algebraic object that is like a vector space, but over a ring instead of a field is called a(n) _________ | |
| Two manifolds are __________ if there exists a smooth map between them with a smooth inverse | |
| The matrix of partial derivatives of a vector-valued function is called the ____________ | |
| The space of all lines through the origin in 3-dimensional space is called ____________ | |
| The problem of finding a function that optimizes some quantity is studied in the field of ___________ | |
| The sigma algebra generated by the open sets of a space is called the ____________ | |
| Lebesgue measure is preferable to the measure induced by the above answer beacuse it is ____________ | |
| Sewing together the boundary circles of two Mobius strips yields a(n) ____________ | |
| The __________ function extends the factorial function to non-integer arguments | |