Topology
2nd Edition
ISBN: 9780134689517
Author: Munkres, James R.
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 4.34, Problem 5E
Let X be a locally compact Hausdorff space. Let Y be the one-point compactification of X. Is it true that if X has a countable basis, then Y is metrizable? Is it true that if Y is metrizable, then X has a countable basis?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Topology
Ch. 4.30 - Show that l and I02 are not metrizable.Ch. 4.30 - Which of our four countability axioms does S...Ch. 4.30 - Which of our four countability axioms does in the...Ch. 4.30 - Let A be a closed subspace of X. Show that if X is...Ch. 4.30 - Prob. 10ECh. 4.30 - Let f:XY be continuous. Show that if X is...Ch. 4.30 - Let f:XY be continuous open map. Show that if X...Ch. 4.30 - Show that if X has a countable dense subset, every...Ch. 4.30 - Show that if X is Lindelof and Y is compact, then...Ch. 4.30 - Give I the uniform metric, where I=[0,1]. Let...
Ch. 4.30 - Prob. 16ECh. 4.30 - Prob. 17ECh. 4.30 - Prob. 18ECh. 4.31 - Show that if X is regular, every pair of points of...Ch. 4.31 - Show that if X is normal, every pair of disjoint...Ch. 4.31 - Show that every order topology is regular.Ch. 4.31 - Prob. 4ECh. 4.31 - Prob. 5ECh. 4.32 - Which of the following spaces are completely...Ch. 4.32 - Prob. 8ECh. 4.32 - Prove the following: Theorem: If J is uncountable,...Ch. 4.32 - Prob. 10ECh. 4.33 - Examine the proof of the Urysohn lemma, and show...Ch. 4.33 - a Show that a connected normal space having more...Ch. 4.33 - Give a direct proof of the Urysohn lemma for a...Ch. 4.33 - Prob. 4ECh. 4.33 - Prob. 5ECh. 4.33 - Prob. 8ECh. 4.34 - Give an example showing that a Hausdorff space...Ch. 4.34 - Give an example showing that a space can be...Ch. 4.34 - Let X be a compact Hausdorff space. Show that X is...Ch. 4.34 - Let X be a locally compact Hausdorff space. Is it...Ch. 4.34 - Let X be a locally compact Hausdorff space. Let Y...Ch. 4.34 - Check the details of the proof of Theorem 34.2.Ch. 4.34 - A space X is locally metrizable if each point x of...Ch. 4.34 - Show that a regular Lindelof space is metrizable...Ch. 4.35 - Show that the Tietze extension theorem implies the...Ch. 4.35 - In the proof of the Tietze theorem, how essential...Ch. 4.35 - Let X be metrizable. Show that the following are...Ch. 4.35 - Let Z be a topological space. If Y is a subspace...Ch. 4.35 - Prob. 5ECh. 4.35 - Let Y be a normal space. The Y is said to be an...Ch. 4.35 - a Show the logarithmic spiral...Ch. 4.35 - Prove the following: Theorem. Let Y be a normal...Ch. 4.36 - Prove that every manifold is regular and hence...Ch. 4.36 - Let X be a compact Hausdorff space. Suppose that...Ch. 4.36 - Let X be a Hausdorff space such that each point of...Ch. 4.36 - Prob. 5ECh. 4.SE - Consider the following properties a space may...Ch. 4.SE - Consider the following properties a space may...Ch. 4.SE - Prob. 3SECh. 4.SE - Consider the following properties a space may...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
What is a Relation? | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=hV1_wvsdJCE;License: Standard YouTube License, CC-BY
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY