Multi-valued function spaces and compactifications of function spaces 集合値関数空間と関数空間のコンパクト化
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著者
書誌事項
- タイトル
-
Multi-valued function spaces and compactifications of function spaces
- タイトル別名
-
集合値関数空間と関数空間のコンパクト化
- 著者名
-
上原, 成功
- 著者別名
-
ウエハラ, シゲノリ
- 学位授与大学
-
筑波大学
- 取得学位
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博士 (理学)
- 学位授与番号
-
甲第2056号
- 学位授与年月日
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1999-03-25
注記・抄録
博士論文
1998
目次
- Contents / (0004.jp2)
- Introduction / p1 (0006.jp2)
- 1. Preliminaries / p7 (0012.jp2)
- §1.1. General definitions and notations / p7 (0012.jp2)
- §1.2. Basic facts on ANR theory / p9 (0014.jp2)
- §1.3. Hilbert space manifolds and Hilbert cube manifolds / p11 (0016.jp2)
- §1.4. Hyperspaces / p13 (0018.jp2)
- §1.5. Spaces of multi-valued functions / p14 (0019.jp2)
- 2. Remarks on absorbers / p16 (0021.jp2)
- §2.1. Comparisons between absorbing pairs / p18 (0023.jp2)
- §2.2. The classification of absorbers / p26 (0031.jp2)
- §2.3. Enlarging absorbers / p28 (0033.jp2)
- 3. A Hilbert cube compactification of the Banach space of real-valued continuous functions / p30 (0035.jp2)
- §3.1. The pairs(C(X),C(X))and(Q,s)are homeomorphic / p32 (0037.jp2)
- §3.2. Remarks and counter-examples / p40 (0045.jp2)
- §3.3. Appendix / p44 (0049.jp2)
- 4. Spaces of multi-valued functions with compact fibers / p46 (0051.jp2)
- §4.1. The space USC(X,Y)for locally connected compacta X and Y / p46 (0051.jp2)
- 5. Hilbert cube manifold local compactifications of some function spaces / p51 (0056.jp2)
- §5.1. A Hilbert cube compactification of H∂(I) / p52 (0057.jp2)
- §5.2. A Q-manifold local compactification of E(I,X) / p56 (0061.jp2)
- §5.3. A Hilbert cube compactification of R(I) / p58 (0063.jp2)
- 6. Spaces of multi-valued function on metric spaces / p62 (0067.jp2)
- §6.1. The converse of Fedorchuk's result / p62 (0067.jp2)
- §6.2. The closedness of USCCB(X) in [数式] / p65 (0070.jp2)
- §6.3. The conditions that USCCB(X) is an AR / p67 (0072.jp2)
- 7. A compactification of multi-valued function spaces / p75 (0080.jp2)
- §7.1. A compactification of multi-valued function spaces on a totally bounded spaces / p77 (0082.jp2)
- §7.2. Supplement / p82 (0087.jp2)
- 8. Multi-valued function spaces homeomorphic to the Hilbert spaces / p85 (0090.jp2)
- §8.1. Relations among CB(X),USCCB(X) and [数式] / p87 (0092.jp2)
- §8.2. The AR-property of USCCB(X)and USCC(X,I) / p91 (0096.jp2)
- §8.3. Multi-valued function spaces homeomorphic to the Hilbert spaces / p95 (0100.jp2)
- §8.4. Remarks on topologies for CB(X) and C(X,I) / p105 (0110.jp2)
- References / p112 (0117.jp2)
