1 U means usual topology on R 2 H means halfopen interval to

1.     U= means usual topology on R

2.     H =means half-open interval topology on R

3.     C =means open half-line topology on R

4.     D= means discrete topology on any set X

5.     I= means indiscrete topology or the trivial topology on any set X

6.     F=finite complement topology on any set X

7.     CC=countable complement topology

Solution

usual topology:

a.open

b.not open

c.not open

d.open

e.open

f.open

g.open

h.open

Half-open interval topology

a.not open

b.not open

c.not open

d.open

e.not open

f.open

g.open

h.open

1. U= means usual topology on R 2. H =means half-open interval topology on R 3. C =means open half-line topology on R 4. D= means discrete topology on any set X

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