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On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line
In this paper we study the maximum number of limit cycles that can
exhibit a planar piecewise linear differential system formed by two pieces
separated by a straight line. More precisely, we prove that this maximum number
satisfies if one of the two linear differential systems has
its equilibrium point on the straight line of discontinuity
Indestructibility of compact spaces
In this article we investigate which compact spaces remain compact under
countably closed forcing. We prove that, assuming the Continuum Hypothesis, the
natural generalizations to -sequences of the selection principle and
topological game versions of the Rothberger property are not equivalent, even
for compact spaces. We also show that Tall and Usuba's "-Borel
Conjecture" is equiconsistent with the existence of an inaccessible cardinal.Comment: 18 page
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