2. Let (Vr) be a topological space. Where Y ={a,6 ,¢ ,d,e } andr={X .®,{c},{d}. {ed} .{d.e} .{e.d.e}, {b,c,a}, {a,b,c,d }}Show that f° ={ {c.d},{d,e},{a,b.c}} is a subbase for thetopology +r.3. Let X ={a,b,c,d,e}, f° ={ {a,b} , {b,c} ,{c,e},fe} } o PX)Find the topology + on X generated by /". 2. Let (X,r) be a topological space. Where X = {a,b,c ,d, e} and1={X,0.{c}.{d}.fe.d}.{d.e}.fc.d.e}.b.c.a}.fa,b.c,d}}.Show that ={{c,d},{d,e}.{a,b,c}} is a subbase for thetopology r. 3. Let X ={a,b,c ,d,e}, B={{a,b},{b.c} .fc.e}.fe}}cP(X )Find the topology r on X generated by ß'.

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Answered: 2. Let (X,r) be a topological space.…

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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2. Let (Vr) be a topological space. Where Y ={a,6 ,¢ ,d,e } and
r={X .®,{c},{d}. {ed} .{d.e} .{e.d.e}, {b,c,a}, {a,b,c,d }}
Show that f° ={ {c.d},{d,e},{a,b.c}} is a subbase for the
topology +r.

3. Let X ={a,b,c,d,e}, f° ={ {a,b} , {b,c} ,{c,e},fe} } o PX)
Find the topology + on X generated by /".

2. Let (X,r) be a topological space. Where X = {a,b,c ,d, e} and
1={X,0.{c}.{d}.fe.d}.{d.e}.fc.d.e}.b.c.a}.fa,b.c,d}}.
Show that ={{c,d},{d,e}.{a,b,c}} is a subbase for the
topology r.

3. Let X ={a,b,c ,d,e}, B={{a,b},{b.c} .fc.e}.fe}}cP(X )
Find the topology r on X generated by ß'.

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