I, Let ¥ ={a,b,c} and B={ {a,c} ,{b,.c} } c P(X). Show thatcannot be a base for any topology r on X .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 /". Exercises 2.11. Let X = {a,b,c} and B={{a,c}.b.c}}cP(X). Show that Bcannot be a base for any topology r on X.2. Let (X,r) be a topological space. Where X {a,b.c,d,e} andr={X ,0,{c},{d}.fe,d}.{d.e} .fc,d.e}.{b.c,a}.fa,b.c,d}}.Show that ={ {c,d}.{d,e}.fa,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 B*.

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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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Question

I, Let ¥ ={a,b,c} and B={ {a,c} ,{b,.c} } c P(X). Show that
cannot be a base for any topology r on X .

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 /".

Exercises 2.1
1. Let X = {a,b,c} and B={{a,c}.b.c}}cP(X). Show that B
cannot be a base for any topology r on X.
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} .fc,d.e}.{b.c,a}.fa,b.c,d}}.
Show that ={ {c,d}.{d,e}.fa,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 B*.

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