devotion & mathematics

  OPEN & CLOSED SETS In this session we see open & closed sets with their properties. OPEN SET : -      A non empty set A in the real line R is called an open set , every point in A is an interior point of A.                                                                     Examples:- * (a, b)  is an open set.  * [a, b] is not open since the end points a, b are not interior points. * Every finite set is not open. * The sets N, Z and Q are not open sets. * The set R of all real numbers is open. * The set of complex numbers |z|<1 is open. * The set of complex numbers |z|  ≤1 is not open. * Every neighbourhood is an open set. Properties of open sets:- 1. Every open set is a union of open intervals. 2. Union of two open sets is open. 3. Intersection of two open sets is ...

  Welcome to " Devotional & Mathematics "!                  I'm B. Viswanadha Phani Sarma ,and I'm here to help you solve problems and to achieve   your goals in mathematics.   This blog is dedicated to exploring the charm and allegence  of mathematics, covering a wide range of topics such as: 👉 Real Analysis 👉 Complex Analysis 👉 Functional Analysis 👉 Topology 👉 Measure Theory ( Lebesgue Theory ) 👉 Algebra  👉 Trigonometry 👉 Geometry 👉 Linear Algebra 👉 Ordinary & Partial Differential Equations and much more.           Together with the topics involves in the lower and higher school level.                         If you're looking for insightful explanations, problem-solving techniques, and deep mathematical discussions, you're in the right place.             Let's embark on this mathemat...