Advanced Math Definitions

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Can you name the Advanced Math Definitions?

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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
The idea of treating an equivalence class of elements as a single element is usually called a(n) __________. (number 5 is one of these)
The Cartesian product of n circles is called the ____________
A group that is also a smooth manifold is called a(n) ____________
A mapping between spaces that preserves distances between elements is called a(n) ____________
A linear map that satisfies the product rule is called a(n) _____________
A complex function that is holomorphic everywhere except an isolated set of poles is called ___________
The rule that allows one to form a set by taking an arbitrary element from each of some family of sets is called the _________________
A(n) ________ commutative ring has only one maximal ideal
A commutative group is more often referred to as being __________
A complete inner product space is called a(n) ____________

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