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Mathematics ( Paper-I ) Metric Spaces & Complex Analysis Book B.Sc 6th Semester U.P

Click below to Buy E-Book Edition:
Buy Latest Mathematics ( Paper -I ) Metric Spaces & Complex Analysis Book in Bilingual Edition ( Both English and Hindi ) Languages for B.Sc 6th Semester Common Minimum Syllabus As Per NEP for All Uttar Pradesh State Universities By Thakur Publication. Written by Experienced Authors | Fast & All India Delivery |
AUTHORS: Dr. Anil kumar Tiwari , Dr. Brijesh Pratap Singh , Dr. Viresh Sharma , Rohit Kushwaha
ISBN : 978-93-5755-766-5
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Click below to Buy E-Book Edition:
Buy Latest Mathematics ( Paper -I ) Metric Spaces & Complex Analysis Book in Bilingual Edition ( Both English and Hindi ) Languages for B.Sc 6th Semester Common Minimum Syllabus As Per NEP for All Uttar Pradesh State Universities By Thakur Publication. Written by Experienced Authors | Fast & All India Delivery |
AUTHORS: Dr. Anil kumar Tiwari , Dr. Brijesh Pratap Singh , Dr. Viresh Sharma , Rohit Kushwaha
ISBN : 978-93-5755-766-5
<td width="41%" valign="top" style="width:41.94%;border-top:none;border-left:none;border-bottom:soli
Part A |
|||
Unit 1: Basic Concepts of Metric Space ¼bdkbZ 1& nwjhd Lkef"V dh ewy vo/kkj.kk,¡½ |
|||
1.1. |
Metric Spaces |
ehfVªd Lisl ¼nwjhd lef"V½ |
13 |
1.1.1. |
Definition |
ifjHkk"kk |
13 |
1.1.2. |
Usual Metric |
çkf;d nwjhd |
17 |
1.1.3. |
Pseudo-Metric |
Nn~e &nwjhd |
21 |
1.1.4. |
Discrete Metric |
fofoDr nwjhd |
22 |
1.1.5. |
Norm Vector Space |
u‚eZ lfn’k Lkef"V |
24 |
1.1.6. |
Quasi Metric Space |
v/kZ nwjhd Lkef"V |
24 |
1.1.7. |
Bounded And Unbounded Metric Space |
ifjc) rFkk vifjc) nwjhd Lkef"V |
25 |
1.2. |
Sequences in Metric Spaces |
nwjhd Lkef"V;ksa esa vuqØe |
27 |
1.2.1. |
Introduction |
ifjp; |
28 |
1.2.2. |
Convergence of the Sequence |
vuqØe dh vfHklkfjrk |
28 |
1.2.3. |
Cauchy Sequences |
d‚ph vuqØe |
30 |
1.2.4. |
Properties of Sequence |
vuqØe ds xq.k |
30 |
1.2.5. |
Theorems |
çes; |
30 |
1.2.6. |
Complete/ Completeness Metric Space |
iw.kZ@iw.kZrk nwjhd Lkef"V |
36 |
1.3. |
Multiple Choice Questions |
cgq fodYih; ç'u |
39 |
|
|
|
|
Unit 2: Topology of Metric Spaces ¼bdkbZ 2& nwjhd Lkef"V dh Vksiksy‚th½ |
|||
2.1. |
Balls or Spheres |
xsansa ;k xksyd |
42 |
2.1.1. |
Open And Closed Ball |
foo`r vkSj lao`r xksyd |
42 |
2.1.2. |
Neighborhood |
çfros’k ;k lkehI; |
43 |
2.2. |
Open Set |
foo`r leqPp; |
46 |
2.2.1. |
Properties of Open Sets |
foo`r leqPp; ds çxq.k |
46 |
2.2.2. |
Interior, Exterior And Frontier Point |
vkarfjd] cká vkSj lhekar fcanq |
50 |
2.2.3. |
Limit And Boundary Point of A Set |
,d leqPp; dh lhek vkSj lhek fcanq |
53 |
2.2.4. |
Derived Set |
O;qRiUu leqPp; |
55 |
2.3. |
Closed Set |
lao`r leqPp; |
59 |
2.3.1. |
Introduction |
ifjp; |
59 |
2.3.2. |
Properties of Closed Set |
lao`r leqPp; ds çxq.k |
59 |
2.3.3. |
Relationship Between The Open And Closed Sets |
foo`r vkSj lao`r leqPp; ds chp laca/k |
63 |
2.3.4. |
Closure of A Set |
leqPp; dk laojd |
65 |
2.3.5. |
Relation Between Interior And Closure of A Set |
fdlh leqPp; ds vkarfjd vkSj laojd ds chp laca/k |
67 |
2.4. |
Product of Matric Spaces |
nwjhd lef"V dk xq.ku |
67 |
2.5. |
Diameter of A Set |
,d leqPp; dk O;kl |
68 |
2.5.1. |
Introduction |
ifjp; |
68 |
2.5.2. |
Distance Between Two Sets |
nks leqPp;ksa ds chp nwjh |
70 |
2.6. |
Cantor’s Theorem |
dSaVj dk çes; |
71 |
2.6.1. |
Introduction |
ifjp; |
71 |
2.6.2. |
Cantor Intersection Theorem |
dSaVj ÁfrPNsnu çes; |
71 |
2.7. |
Subspaces |
milef"V |
73 |
2.8. |
Dense Set |
l?ku leqPp; |
74 |
2.9. |
Multiple Choice Questions |
cgq fodYih; ç'u |
79 |
2.10. |
Exercise |
vH;kl |
80 |
Unit 3: Continuity & Uniform Continuity in Metric Spaces ¼bdkbZ 3& nwjhd lef"V esa lkarR;rk vkSj ,dleku lkarR;rk½ |
|||
3.1. |
Continuity In Metric Spaces |
nwjhd lef"V esa lkarR;rk |
82 |
3.1.1. |
Limit of Functions |
Qyuksa dh lhek |
82 |
3.1.2. |
Continuity of Function |
Qyu dh lkarR;rk |
82 |
3.1.3. |
Mapping |
çfrfp=.k |
86 |
3.1.4. |
Continuous Mapping |
larr çfrfp=.k |
86 |
3.1.4.1. |
Locally Continuous Mapping |
LFkkuh; :i ls larr çfrfp=.k |
87 |
3.1.4.2. |
Composition of Continuous Mapping |
larr çfrfp=.k dh lajpuk |
88 |
3.1.5. |
Topological Mapping |
Vksiksy‚ftdy çfrfp=.k |
88 |
3.1.6. |
Topological Equivalence |
Vksiksy‚ftdy rqY;rk |
88 |
3.1.7. |
Sequential Criterion |
vuqØfed ekunaM |
89 |
3.1.8. |
Characterizations of Continuity |
lkarR;rk ds y{k.k |
90 |
3.2. |
Uniform Continuity |
,dleku lkarR;rk |
92 |
3.3. |
Homeomorphism |
le:irk |
95 |
3.3.1. |
Introduction |
ifjp; |
95 |
3.3.2. |
Homeomorphic Spaces |
gksfe;ksekWfQZd lef"V |
96 |
3.4. |
Fixed Point Theorems |
fuf'pr fcanq çes; |
97 |
3.4.1. |