MTH634 Assignment 2 Solution Fall 2022 || mth634 assignment solution

MTH634 Assignment 2 Solution Fall 2022 || mth634 assignment solution

MTH634 Assignment 2 Solution Fall 2022 || mth634 assignment solution

First Part
Let X = fa, b, c, d, ef and let A = {{a, b, d}, {d, c}, {c, e}, x} be a subbase. To find the
 base B
generated by A, we need to take all possible unions of elements in A.
B {AUBIA, BEA}
- {(la, b, d} u fd, c}). (d. c}u fc, e}). ((c, e) ux), (la, b, d) u {d. c} u fc, e} ux)}
= tta, b, c, d, fc, d, el, la, b, c, d, e}}
The topology generated by B is the collection of all subsets of X that can be formed by
taking arbitrary unions of elements in B. In other words, it is the collection of all 
subsets of Xx that
can be formed by taking arbitrary unions of the sets in B.
Topology= {scxIS = U: UU U.. U U., U, U, , U, E B}
Second Part:
Let a= {fab.cl.lc.a).lde}} be a subbase. To find the base generated by a, we need to
take all possible unions of elements in a.
B=lauBla, Be a}
= {((abc) u fcd}), (cd} u {de}). ({abc)u {cd} u (de}}
={labcd). cdel, (abcdel}
The topology generated by Bis the collection of all subsets of X that can be formed by
taking arbitrary unions of elements in B. In other words, it is the collection of all subsets of X that
can be formed by taking arbitrary unions of the sets in .
Topology= {sCXIS = U uU U..uU, U, U, . U, e B}
x