Solutions for Topology
Problem 1E:
Define two points (x0,y0) and (x1,y1) of the plane to be equivalent if y0x02=y1x12. Check that this...Problem 2E:
Let C be a relation on a set A. If A0A, define the restriction of C to A0 to be the relation...Problem 3E:
Here is a proof that every relation C that is both symmetric and transitive is also reflexive: Since...Problem 4.1E:
Let f:AB be a surjective function. Let us define a relation on A by setting a0a1 if f(a0)=f(a1)....Problem 4.2E:
Let f:AB be a surjective function. Let us define a relation on A by setting a0a1 if f(a0)=f(a1). Let...Problem 5.1E:
Let S and S be the following subsets of the plane: S={(x,y)y=x+1and0x2},S={(x,y)yxisaninteger} a...Problem 5.2E:
Let S and S be the following subsets of the plane: S={(x,y)y=x+1and0x2},S={(x,y)yxisaninteger} b...Problem 5.3E:
Let S and S be the following subsets of the plane: S={(x,y)y=x+1and0x2},S={(x,y)yxisaninteger} c...Problem 6E:
Define a relation on the plane by setting (x0,y0)(x1,y1) If either y0x02y1x12, or y0x02=y1x12 and...Problem 8E:
Check that the relation defined in Example 7 is an order relation. EXAMPLE 7 Consider the relation...Problem 10.1E:
a Show that the map f:(1,1) of Example 9 is order preserving. EXAMPLE 9 The interval (1,1) of real...Problem 13E:
Prove the following: Theorem. If an ordered set A has the least upper bound property, then it has...Browse All Chapters of This Textbook
Chapter 1.1 - Fundamental ConceptsChapter 1.2 - FunctionsChapter 1.3 - RelationsChapter 1.4 - The Integers And The Real NumbersChapter 1.5 - Cartesian ProductsChapter 1.6 - Finite SetsChapter 1.7 - Countable And Uncountable SetsChapter 1.8 - The Principle Of Recursive DefinitionChapter 1.9 - Infinite Sets And The Axiom Of ChoiceChapter 1.10 - Well-ordered Sets
Chapter 2.13 - Basis For A TopologyChapter 2.16 - The Subspace TopologyChapter 2.17 - Closed Sets And Limit PointsChapter 2.18 - Continuous FunctionsChapter 2.19 - The Product TopologyChapter 3.24 - Connected Subspaces Of The Real LineChapter 3.28 - Limit Point CompactnessChapter 3.29 - Local CompactnessChapter 3.SE - Supplementary Exercises: NetsChapter 4.30 - The Countability AxiomsChapter 4.31 - The Separation AxiomsChapter 4.32 - Normal SpacesChapter 4.33 - The Urysohn LemmaChapter 4.34 - The Urysohn Metrization TheoremChapter 4.35 - The Tietze Extension TheoremChapter 4.36 - Imbeddings Of ManifoldsChapter 4.SE - Supplementary Exercises: Review Of The Basics
Sample Solutions for this Textbook
We offer sample solutions for Topology homework problems. See examples below:
More Editions of This Book
Corresponding editions of this textbook are also available below:
Topology
2nd Edition
ISBN: 9780131816299
Topology: Pearson New International Edition
2nd Edition
ISBN: 9781292023625
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