differential geometry w notes from teacher_Part_4

differential geometry w notes from teacher_Part_4 - 1.2....

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: 1.2. MANIFOLDS 7 Definition 1.2.1 A general topological space is a set M together with a collection of subsets of M, called open sets , that satisfy the following properties 1. M and are open, 2. the intersection of any finite number of open sets is open, 3. the union of any collection of open sets is open. Such a collection of open sets is called a topology of M. A subset of M is closed if its complement M \ F is open. The closure S of a subset S M of a topological space M is the intersec- tion of all closed sets that contain S ; it is equal to S = S S . A subset S M of a topological space is dense in M if S = M , that is, every non-empty subset of M contains an element of S . A topological space is called separable if it contains a countable dense subset. A topology on M naturally induces a topology on any subset of M . Let A M be a subset of M . Then the induced topology on A is defined as follows. A subset V A is defined to be open subset of...
View Full Document

Page1 / 2

differential geometry w notes from teacher_Part_4 - 1.2....

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