alexa On Equivalent Conditions for Compactness in Metric Spa
ISSN ONLINE(2319-8753)PRINT(2347-6710)

International Journal of Innovative Research in Science, Engineering and Technology
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Research Article

On Equivalent Conditions for Compactness in Metric Spaces

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In this paper the comparison of two types of conditions (A) and (B) on a topological space is made. It is proved that the condition (A) is equivalent to (B) and normality of the topological space. Furthermore pre compactness is a necessary condition for (A) on a uniform space. Condition (A):- For any two disjoint closed sets at least one is compact. Condition (B):- For any two normally separable closed sets at least one is compact. Further it is proved that in metric spaces, these conditions (A) and (B) are equivalent to compactness


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