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...it. Not every topological space is uniformizable; for example, non-regular spaces. [[Category:Topological spaces with richer structure]]

...if every net (cf. [[Net (of sets in a topological space)|Net (of sets in a topological space)]]) in $X$ has a Cauchy subnet. Therefore, for $X$ to be a pre-compac [[Category:Topological spaces with richer structure]]

''in a topological linear space $X$'' ...ly-compact sets have applications in the theory of approximation in Banach spaces; they have the property that an [[element of best approximation]] exists. A

...ct convex sets (cf. [[Convex set]]) $F$ in a Euclidean space $E^n$ endowed with the [[Hausdorff metric]]: ...sets (other metrizations, non-compact sets, classes of sets, other initial spaces) see [[#References|[1]]].

...t can be viewed as the appropriate extension of homotopy theory to general spaces. ...imate fibrations and shape fibrations, imbeddings of compacta in Euclidean spaces and in exact homology theories.

[[Category:Topological spaces with richer structure]] Generalizations of metric spaces (cf. [[Metric space|Metric space]]), in which the distances between points

a set with a uniform structure defined on it. A uniform structure (a X\textrm { with }(x,z)\in W, (z,y)\in W\}$.

...ls into three parts: 1) the introduction and study of infinite-dimensional spaces as such; 2) the study of the simplest functions, namely, when $ x $ ...sely interpreted as infinite-dimensional matrices) on infinite-dimensional spaces.

...colour, etc.). In its subsequent stages of development geometry also dealt with other relations and shapes of reality, similar to spatial shapes. In our ow ...ennium B.C.). In those days geometric postulates were formulated as rules, with primitive logical proofs or without any proofs at all. During the period be