2. Let X = (a, b, c, d, e} and t = {(O, {a, c, d), (b, c, d, e), (a), (C, d), X) then subbase of (X, T) is OB - (0, X) OB = {{a.). (b), (c). (d), (e}} OB= {{a.), (a. c, d), (b, c, d. e})
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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(2)
Given a set, and .
To find the sub-base of .
A set S is said to be a sub-base of a topology, , if finite intersections of elements of S forms a basis for .
(a) B =
Then, the corresponding basis is,
.
By considering the unions of every elements of B', then X and is only formed.
Therefore, B' does not forms the basis.
Therefore, B is not a sub-base.
Hence, (a) is not true.
(b)
Then, the corresponding basis is,
Every element of is formed by the union elements of B'.
Therefore, B' is a basis.
Therefore, B is a sub-base.
(c)
Then, the corresponding basis is,
Every element of is formed by the union elements of B'.
Therefore, B' is a basis.
Therefore, B is a sub-base.
Therefore, (b) and (c) are sub-bases.
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