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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.
The finest topology on X is the discrete topology; this topology makes all subsets open. The coarsest topology on X is the trivial topology; this topology only admits the empty set and the whole space as open sets. In function spaces and spaces of measures there are often a number of possible topologies.
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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English: Examples and non-examples of topological spaces, based roughly on Figures 12.1 and 12.2 from Munkres' Introduction to Topology.The 6 examples are subsets of the power set of {1,2,3}, with the small circle in the upper left of each denoting the empty set, and in reading order they are:
This property has nothing to do with topology as such, but only set theory. Each of the following properties is stricter than disjointness, incorporating some topological information. The properties below are presented in increasing order of specificity, each being a stronger notion than the preceding one.
The Stone–Čech compactification of the topological space X is a compact Hausdorff space βX together with a continuous map i X : X → βX that has the following universal property: any continuous map f : X → K, where K is a compact Hausdorff space, extends uniquely to a continuous map βf : βX → K, i.e. (βf)i X = f.
In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets.In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connected subsets.