Next semester, I'll be taking a course in advanced calculus in my uni. I need a book which is beginner friendly, suitable for self study and most importantly covers the topics below.
1.The Real line and Euclidean space (ordered field, distance, Schwarz Inequality)
The topology of Euclidean space; open sets, Interior of a set, closed sets
The topology of Euclidean space; accumulation points, closure of a set, boundary of a set, sequences, completeness
Compact and Connected sets; compactness, the Heine-Borel theorem,
Compact and Connected sets; Nested set property, Path-connected sets, Connected sets
Continuous Mappings; continuity, Images of compact and connected sets
Continuous Mappings; operations on continuous mappings, the Boundedness of continuous functions on compact sets
Continuous Mappings; Uniform continuity
Uniform convergence; Differentiation and Integration of functions of one variable
Pointwise convergence, the Weierstrass M-test Uniform convergence
Integration and differentiation of series Uniform convergence;
The space of continuous functions,
The Arzela - Ascoli theorem
Thanks in advance.