4. Let E=]0,4[U]5, 6[ . (a) Prove that xo (b) Decide whether E is open, closed or compact, and determine the 3 is an interior point of E. • set E° of the interior points of E, • set ƏE of the boundary points of E , • set E' of the limit points of E and • the closure E of E.

4. Let E=]0,4[U]5, 6[ . (a) Prove that xo (b) Decide whether E is open, closed or compact, and determine the 3 is an interior point of E. • set E° of the interior points of E, • set ƏE of the boundary points of E , • set E' of the limit points of E and • the closure E of E.

Name: 4. Let E=]0,4[U]5, 6[ .(a) Prove that xo(b) Decide whether E is open,
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Description: 4. Let E=]0,4[U]5, 6[ .(a) Prove that xo(b) Decide whether E is open, closed or compact, and determine the3 is an interior point of E.• set E° of the interior points of E,• set dE of the boundary points of E,• set E' of the limit points of E and• th

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Let E=]0,4[U]5, 6[ .
(a) Prove that xo
(b) Decide whether E is open, closed or compact, and determine the
3 is an interior point of E.
• set E° of the interior points of E,
• set dE of the boundary points of E,
• set E' of the limit points of E and
• the closure E of E.

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Step 1: Definition used and given.

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Step 2: Show that 3 is an interior point of E.

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Step 3: Find the interior points of E.

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Step 4: Find the boundary points of E.

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Step 5: Find set of limit points of E.

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Step 6: Find the closure of E.

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