Answer for Munkres Topology Problem 17.18 - Share Your Solution!

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SUMMARY

The discussion revolves around solving problem 17.18 from Munkres' "Introduction to Topology." Participants emphasize the importance of demonstrating an attempt at the problem before sharing solutions. The key focus is on identifying the base of open sets in the ordered square and determining if every basic open set containing a point x intersects a given set A.

PREREQUISITES
  • Understanding of basic topology concepts, particularly open sets.
  • Familiarity with Munkres' "Introduction to Topology" textbook.
  • Knowledge of ordered topological spaces.
  • Ability to analyze intersections of sets in a topological context.
NEXT STEPS
  • Review Munkres' "Introduction to Topology" for foundational concepts.
  • Study the properties of ordered topological spaces.
  • Practice problems related to open sets and their bases.
  • Explore the concept of intersections in topology with practical examples.
USEFUL FOR

Students of topology, educators teaching Munkres' material, and anyone seeking to deepen their understanding of open sets and ordered spaces in topology.

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Would anyone care to share their answer for problem 17.18 in munkres intro topology book?
no need for indepth explanation, just the answer will work (computational problem).
 
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Fisicks said:
Would anyone care to share their answer for problem 17.18 in munkres intro topology book?
no need for indepth explanation, just the answer will work (computational problem).
The policy here is that you have to show your attempt to solve the problem first.
 
Come on, it's not so difficult. Can you give me a base of the open sets of the ordered square?

For A (and for all the rest), you'll need to check for each point x whether every basic open set that contains x, will intersect A.
 

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