Introduction to Topology — Solutions to Mendelson (selected problems)
Topology studies properties of spaces preserved under continuous deformation. Below is a concise set of worked solutions and guidance for selected exercises from Elliot Mendelson’s Introduction to Topology (commonly used problems from early chapters). These notes assume basic familiarity with sets, functions, and proofs by contradiction/induction.
Exercise 2.3
Key Capabilities
- Problem statement lookup (chapter + number)
- Warm-up – recalls relevant definitions (open set, neighborhood, closure, continuous, etc.)
- Proof scaffolding – fills in missing steps with user interaction
- Counterexample hints – suggests finite/indiscrete/discrete spaces where appropriate
- Similar problem recommendation – e.g., “This is like Ex. 6, §3.1”
- Check my proof – user pastes their attempt, tool flags leaps or missing cases
Summary Table of Key Results from Mendelson
| Chapter | Theorem | Page reference (approx.) | |---------|---------|--------------------------| | 2 | Every metric space is Hausdorff | 48 | | 3 | Subspace topology basis = intersections | 78 | | 4 | Homeomorphism preserves compactness, connectedness | 110 | | 5 | Path-connected ⇒ connected | 135 | | 6 | Continuous image of compact is compact | 165 |
Overview of the Book
The book is divided into three main sections:
Introduction To Topology Mendelson Solutions Patched
Introduction to Topology — Solutions to Mendelson (selected problems)
Topology studies properties of spaces preserved under continuous deformation. Below is a concise set of worked solutions and guidance for selected exercises from Elliot Mendelson’s Introduction to Topology (commonly used problems from early chapters). These notes assume basic familiarity with sets, functions, and proofs by contradiction/induction.
Exercise 2.3
Key Capabilities
Summary Table of Key Results from Mendelson
| Chapter | Theorem | Page reference (approx.) | |---------|---------|--------------------------| | 2 | Every metric space is Hausdorff | 48 | | 3 | Subspace topology basis = intersections | 78 | | 4 | Homeomorphism preserves compactness, connectedness | 110 | | 5 | Path-connected ⇒ connected | 135 | | 6 | Continuous image of compact is compact | 165 | Introduction To Topology Mendelson Solutions
Overview of the Book
The book is divided into three main sections: Problem statement lookup (chapter + number) Warm-up –
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@jamal Are you downloading the caption track of a video which belongs to you? You cannot download caption tracks of videos belonging to other people. Also please check your credentials if they are being passed with the right parameters.
Is there another way to download subtitles for any YouTube video?
No not really. The API does not allow downloading of captions for videos which do not belong to the current user.
Thank you
I found this site diycaptions.com but I want the way it works its not needing youtube api
They must be using some other method. This blog post is only about the Youtube API way of downloading a caption file.