MATH 4565 Midterm: MATH4565-sp16-midterm
31 Jan 2019
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Midterm exam: a space x is said to be homogeneous if, for every two points x1, x2 x, there is a self-homeomorphism f : x x such that f (x1) = x2. That is to say, if x is homeomorphic to y , and x is homogeneous, then y is also homogeneous: let (x, t ) be a topological space. An arithmetic progression is a subset of the form. Aa,b = {a + nb | n z}, with a, b z and b 6= 0. (a) prove that the collection of arithmetic progressions, Spring 2016: let f : x y be a continuous map. We say that f is proper if f 1(k) is compact, for every compact subset k y . C be a closed subspace of y , and let u be an open neighborhood of f 1(c) in.
