# Let X be a set with infinite c

Let X be a set with infinite cardinality. Define Tx ={U ⊆ X : U = Ø or X \ U is finite}. Prove that Tx is atopology on X. (Tx is called the Cofinite Topology orFinite Complement Topology.)

be a set with infinite cardinality .

or \ is finite} .

Defination : A collection of subsets of is said to form a tpology on if it satisfies the following three conditions .

If be an finite collection  then

If  be an infinite collection then

Now we will prove that the collection or \ } is finite forms a topology on .

by defination of .

Also as \ is a finite set .

Suppose be a finite collection of elements of .

are all finite set .

is a finite set as finite union of finite set is finite.

is a finite set .

suppose  be an infinite collection of elements of .

are all finite set .

is a finite set as arbitrary intersection of finite set is finite.

is a finite set .

So satisfies all three conditions to be a topology on Hence the collection or \ is finite } is a topology on

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"

Pages (275 words)
Standard price: \$0.00
Client Reviews
4.9
Sitejabber
4.6
Trustpilot
4.8
Our Guarantees
100% Confidentiality
Information about customers is confidential and never disclosed to third parties.
Original Writing
We complete all papers from scratch. You can get a plagiarism report.
Timely Delivery
No missed deadlines – 97% of assignments are completed in time.
Money Back