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A Set 
for which a Topology 
has been specified is called a topological space (Munkres 1975, p. 76).
See also Kuratowski's Closure-Component Problem, Open Set, Topological Vector Space
References
Berge, C. Topological Spaces Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity.
New York: Dover, 1997.
Munkres, J. R. Topology: A First Course. Englewood Cliffs, NJ: Prentice-Hall, 1975.