hmwk6 - MATH 202A HOMEWORK 6 This assignment is due Wed.,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 202A HOMEWORK 6 This assignment is due Wed., Oct. 10. The topics addressed are connectedness, products and quotients. Problem 1 . (a) Let X be a topological space, { C } be a collection of connected subsets such that any two of them have a point in common. Prove that G = [ C is connected. [It follows that our definition of connected component containing x is connected, and is the largest connected set containing x .] (b) Let X be a topological space and Y X . Prove that if Y is connected, then Y is connected. [It follows that the connected components of any topological space are closed.] (c) Prove that the components of a locally connected topological space are open. (d) Prove that the topologists sine curve is not path connected. [In class, we proved that it is connected.] (e) Find an example of a connected space with 3 path connected components. (f) Prove that the Cantor set is totally disconnected. (g) Prove that R 2 \ Q 2 is connected....
View Full Document

Page1 / 2

hmwk6 - MATH 202A HOMEWORK 6 This assignment is due Wed.,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online