Let X be a set with infinite cardinality. Define Tx = {U ? X : U...

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Advance Math

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

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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 See Answer

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Let X be a set with infinite cardinality. Define Tx = {U ? X : U...

50.1K

Verified Solution

Question

Advance Math

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

Answer & Explanation Solved by verified expert

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Let X be a set with infinite cardinality. Define Tx = {U ? X : U...

50.1K

Verified Solution

Question

Advance Math

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.)

Answer & Explanation Solved by verified expert

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