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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.
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}}
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The converse does not hold. For example, the product of continuum-many closed intervals [,] with the product topology is compact and hence countably compact; but it is not sequentially compact. [5] For first-countable spaces, countable compactness and sequential compactness are equivalent. [6]
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.
The cofinite topology on an infinite set is locally compact in senses (1), (2), and (3), and compact as well, but it is not Hausdorff or regular so it is not locally compact in senses (4) or (5). The indiscrete topology on a set with at least two elements is locally compact in senses (1), (2), (3), and (4), and compact as well, but it is not ...
The K-topology on R is the topology obtained by taking as a base the collection of all open intervals (,) together with ... Munkres, James R. (2000). Topology (2nd ed.).
In mathematics, especially topology, a perfect map is a particular kind of continuous function between topological spaces. Perfect maps are weaker than homeomorphisms , but strong enough to preserve some topological properties such as local compactness that are not always preserved by continuous maps.
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