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- W4249318217 abstract "We briefly recall here the two key theorems about continuous functions used in the book. Recall that a subset of a topological space is relatively compact (resp. relatively sequentially compact) if its closure is compact (resp. sequentially compact). Also, compactness and sequential compactness are equivalent notions for metric spaces. The first theorem concerns the relative compactness in the space C([0, T];ℛ d ) of continuous functions [0, T] → ℛ d for a prescribed prescribed T > 0. C([0, T];ℛ d ) is a Banach space under the ‘sup-norm’ <math display='block'> <mrow> <mrow><mo>‖</mo> <mi>f</mi> <mo>‖</mo></mrow><mover> <mstyle mathsize='140%' displaystyle='true'><mo>=</mo></mstyle> <mrow> <mi>d</mi><mi>e</mi><mi>f</mi> </mrow> </mover> <msub> <mrow> <mi>sup</mi> </mrow> <mrow> <mi>t</mi><mo>∈</mo><mrow><mo>[</mo> <mrow> <mn>0</mn><mo>,</mo><mi>T</mi> </mrow> <mo>]</mo></mrow> </mrow> </msub> <mrow><mo>‖</mo> <mrow> <mi>f</mi><mrow><mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </mrow> <mo>‖</mo></mrow> </mrow> </math> $$left| f right|mathop = limits^{def} {sup _{t in left[ {0,T} right]}}left| {fleft( t right)} right|$$ . That is," @default.
- W4249318217 created "2022-05-12" @default.
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- W4249318217 date "2008-01-01" @default.
- W4249318217 modified "2023-10-18" @default.
- W4249318217 title "Appendices" @default.
- W4249318217 doi "https://doi.org/10.1007/978-93-86279-38-5_11" @default.
- W4249318217 hasPublicationYear "2008" @default.
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