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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Our main result says that if a product space is sgcompact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete.
📌 3 Key Takeaways
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Objective & Hypothesis:The aim of this paper is to continue the study of sg-compact spaces.
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Key Findings & Data:The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces.
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Conclusion & Impact:Our main result says that if a product space is sgcompact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:sg-compact · Hereditarily compact · C2-space
Abstract
The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main result says that if a product space is sgcompact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete.
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Cite This Article
Dontchev, J., Ganster, M. (2005). ON A STRONGER FORM OF HEREDITARY COMPACTNESS IN PRODUCT SPACES. Hacettepe Journal of Mathematics and Statistics, Volume: 34 Special Issue. https://ajindex.com/articles/1403836