위상공간의 특성에 관한 연구 = A Study on the Characteristics of Topological Space

다국어 초록 (Multilingual Abstract)

In this theses, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it.
A topological space(X, T) has A-form iff the empty set is the only subset which is both closed and compact set.
The following condition is equivalent:
1)(X, T) has a closed and compact subset which is the only empty set.
2)For every open set U≠X, there is X=∪{} which is a chain ={} of a open set which is U⊊U≠X.
And For every point x∈X, {} has a closed proper subset which is non-empty.