Continuous Transformations in Analysis With an Introduction to Algeb
The general objective of this treatise is to give a systematic presenta tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought
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Complement C 1.1.1. Complete space 1.1.4. Completely additive family 1.1.4. Component 1.1.3. Condition (arg) V!. 1.2. Condition (arg, r) V1.1.2. Condition (N) IV.1.4. Condition (V) II1.1.i. Connected 1.1.3. Continuous 1.1.3, 1.1.5. Continuum 1.1.3. Convex I.2.2. Covering I. 1. 3. Crude multiplicity function 1.1.2.
Da(u, T) IV.S.1. De(u, T), D;(u, T), D;(u, T) IV.4.1, IV.4·3. Deformation retract 1.1.5. Ll(n, m), Ll*(n, m) I.2.3. Dense 1.1.3. Derivative III.2.3. Determining system 1.1.4. Diameter I. 1.4. Differential III.i.3. Disconnected I.1.3. Domain I.1.3.
eA C IV.4.2. eBV IV.4.1. E(T. D), EP(T, D), Ei(T, D), Ef(T, D) 11.3.6. (};(x, T, D), (};i(x, T, D) II.3.3. En 1.2.2. e (x, E) 1.1.4. e.m.m.C. II.3.3. Essential absolute continuity IV.4.2. Essential bounded variation IV.4.1. Essential generalized Jacobian IV.4.3. Essentially isolated II.3.3. Essential local index Il.3.4.
440 Essential maximal model continuum II.3.3. Essential sets II.3.6. Essential total variation IV.4.1. Exact 1.3.3. Finite measure II1.1.2. Formal complex 1.5.2, 1.5.5. Frame II. 1. 1. Frontier (fr) 1.1.3. Fully normal 1.1.3. Generalized Lipschitzian V.3·6. HAUSDORFF space 1.1.3. Homeomorphism 1.1.5. Homotopy, homotopic 1.1.5, 1.4.5. Hypothesis Ho V1.3.4. I 1.3.1. iB (u, T) 11.3.7. ie(C, T) II.3.4. Inclusion mapping 1.1.1Indicator domain II.3.2. Indicator system 11.3.2. Interior (int) 1.1.3.
J(u, T) V.2.2. IV.5.3. IVA.3. JORDAN region VI. 1. 1.
Is (u, T) f e (u, T)
k (x, T, D) II.3.3. K(x, T, D), K+(x, T, D), K-(x, T, D)
Index. Metric space 1.1.4. m.m.c. II.3.1. fl- (x, T, D) II.2.2. fl-. (x, T, D) 11.3.4. n-cell E" 1.2.2. n-interva~ 1.2.2. n-sphere Sn 1.2.2. N(x, T, 5) 1.1.2. Negative indicator domoain 11.3.2. Negative indicator system II.3.2. Normal 1.1.3. VB IV.5.1. ve IV.4.1. v-integral III. 1.2. v-summable III. 1.2. Open covering 1.1.3. Open set 1.1.3. Ordinary Jacobian V.2.2. Oriented n-cube 1.2.2. Oscillation w 1.1.2, 1.1.5, V.1.1. Pair 1.1.1. Parallelotope 1.2.2. Partition AlB 1.1.3. Point of density III. 1. 1. Point of linear density III. 1 .1. Positive indicator domain II.3.2. Positive indicator system 11.302. Preferred generator 11.1.3. p-coboundary 1.4.1. p-cochain 104.1. p-cocyde 1.4.1. p-function 1.5.1.
II.3·2.
Sf (D), Sf+(D), Sf-(D) IVA.1, IVA.3. LEBESGUE integral, measure II1.1.1L-measurable III.1.1. L-summable III. 1. 1. Lipschitzian III.1.3, V.2.3. Locally connected 1.1.3. Lower semi-continuous 1.1.3.
Rn 1.2.1. Reduced base-set IV.2.1. Refinement 1.1.3. Regular determining system 1.1.4. Relatives 11.3.7. Retract, retraction 1.1. 5. e(T1 , T 2 , E) 1.1·5·
sn
M(X, A), M(X) 1.6.1. MAYER complex 1.4.1. Maximal model continuum II.3.1. Measurable homeomorphism IVA.6.
1.2.2. sA CB IV.5.3. sBVB IV.5.3. @)(x, T, D), @)+(x, T, D), @)-(x, T, D)
11.3.2.
Index. Segment 1.2.2. Separable 1.1.3. Simple arc VI. 1. 1. Singular measure III. 1.2. Spherical frame I1.2.1. Standard triple 1.4.3. Star 1.1.3. Star refinement 1.1.3. Stereographic projection 1.2.2. Strongly adjacent 1.2.3. Strongly connected 1.2.3. Sub-additive 111.2.3. II
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