Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space...Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space, 2x denotes all nonempty closed subset with finite topology in X.展开更多
In this letter we raise three special nearnesses called s-nearness, p-nearness and w-nearness. We obtain one to one correspondence between strongly paracompactification and s-nearness, paracompactification and p-nearn...In this letter we raise three special nearnesses called s-nearness, p-nearness and w-nearness. We obtain one to one correspondence between strongly paracompactification and s-nearness, paracompactification and p-nearness and weakly paracompactification and w-nearness respectively. Definition 1. Let （X） be a family of all the subsets of a topological space X and （X）, ∈ S（X） iff there exists an 0 = {Aa: a ∈ A}such that for each a ∈ A, X\（A0∪Aa） , here A is an ordinal number and Definition 2. A nearness v on a T1-space展开更多
文摘Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space, 2x denotes all nonempty closed subset with finite topology in X.
文摘In this letter we raise three special nearnesses called s-nearness, p-nearness and w-nearness. We obtain one to one correspondence between strongly paracompactification and s-nearness, paracompactification and p-nearness and weakly paracompactification and w-nearness respectively. Definition 1. Let （X） be a family of all the subsets of a topological space X and （X）, ∈ S（X） iff there exists an 0 = {Aa: a ∈ A}such that for each a ∈ A, X\（A0∪Aa） , here A is an ordinal number and Definition 2. A nearness v on a T1-space
