Parakompakt uzaylar
Paracompact spaces
- Tez No: 216346
- Danışmanlar: DOÇ. DR. MURAT DİKER
- Tez Türü: Yüksek Lisans
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Cover, Open cover, Compact, Paracompact, Countable paracompact, weakly paracompact, strongly paracompact, locally finite family, c-locally finite fam-ily, c-discrete family, point-finite family, partition of unity
- Yıl: 2007
- Dil: Türkçe
- Üniversite: Hacettepe Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 86
Özet
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Özet (Çeviri)
This work consists of four chapters.The first chapter contains some well-known notions which are related to paracom-pact spaces, and important results as Vedenissoff, Kuratowski, and Baire Category Theorems which will be used in the sequel.The second chapter is devoted to some basic properties of covers and paracompact-ness. In particular, the characterisations of paracompactness are given in terms of partition of unity, c-locally finite and barycentric families. Further, it is shown that the paracompactness is preserved under closed continuous functions.In the third chapter, the countable paracompactness is presented and using star finite and point-finite families, a well-known characterisation of a normal countable paracompact space is given. Further, countable paracompactness spaces is discussed in product topology.In chapter four, weakly and strongly-paracompactness are considered and the Michael Nagami, and Worrell Theorems are given. Finally, under regularity assumption, a characterisation for strongly paracompactness is presented.
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