2. Let (X,r) be a topological space. Where X {a,b.c,d,e} and r={X,0.{c}.{d}.fe,d}.{d.e}.fe.d.e},fb.c,a}. {a,b,c,d}}. Show that 6 ={ {c,d}.{d,e}.{a,b.c}} is a subbase for the topology r.
2. Let (X,r) be a topological space. Where X {a,b.c,d,e} and r={X,0.{c}.{d}.fe,d}.{d.e}.fe.d.e},fb.c,a}. {a,b,c,d}}. Show that 6 ={ {c,d}.{d,e}.{a,b.c}} is a subbase for the topology r.
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 /".

Transcribed Image Text: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.

Transcribed Image Text: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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