Search results
Results from the WOW.Com Content Network
James Raymond Munkres (born August 18, 1930) is a Professor Emeritus of mathematics at MIT [1] and the author of several texts in the area of topology, including Topology (an undergraduate-level text), Analysis on Manifolds, Elements of Algebraic Topology, and Elementary Differential Topology. He is also the author of Elementary Linear Algebra.
Download as PDF; Printable version; ... for instance in algebraic topology, in complex analysis, and in modeling. ... James R. Munkres: . Band 1984. Addison Wesley ...
Add the following into the article's bibliography * {{Munkres Topology|edition=2}} and then add a citation by using the markup Some sentence in the body of the article.{{sfn|Munkres|2000|pp=1-2}}
Pavel Urysohn. In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma [1]) states that any real-valued, continuous function on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
If and are topological spaces and is the product space, endowed with the product topology, a slice in is a set of the form {} for . A tube in X × Y {\displaystyle X\times Y} is a subset of the form U × Y {\displaystyle U\times Y} where U {\displaystyle U} is an open subset of X {\displaystyle X} .
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate
As a less trivial example, consider the space of all rational numbers with their ordinary topology, and the set of all positive rational numbers whose square is bigger than 2. Using the fact that 2 {\displaystyle {\sqrt {2}}} is not in Q , {\displaystyle \mathbb {Q} ,} one can show quite easily that A {\displaystyle A} is a clopen subset of Q ...
Let be a set and a nonempty family of subsets of ; that is, is a nonempty subset of the power set of . Then is said to have the finite intersection property if every nonempty finite subfamily has nonempty intersection; it is said to have the strong finite intersection property if that intersection is always infinite.