Search results

...copies of a two-point space with the [[discrete topology]]. It is thus [[compact space|compact]]. It may be realised as the space of binary sequences As a topological space, the Cantor set is [[uncountable set|uncountable]], [[compact space|compact]], [[second countable space|second countable]] and [[totally discon

...ral topology]], a '''compactification''' of a [[topological space]] is a [[compact space]] in which the original space can be embedded, allowing the space to be stu ...if ''X'' is a [[Tychonoff space]] then any continuous map from ''X'' to a compact space can be extended to a map from β(''X'') compatible with ''e''. This extens

...ates that a subset of the [[Euclidean space]] '''R'''^''n'' is [[compact space|compact]] if and only if it is [[closed set|closed]] and bounded.

{{r|Compact space}}

{{r|Compact space}}

{{r|Compact space}}

{{r|Compact space}}

{{r|Compact space}}

* [[Tychonov's Theorem]]: The product of a family of non-empty [[compact space|compact topological space]]s is compact in the [[product topology]].

The product of two (and hence finitely many) [[compact space]]s is compact.

* [[Compact space|Compactness]];

{{r|Compact space}}

{{r|Compact space}}

{{r|Compact space}}

...'''^d. He showed that such a system of functions has a unique [[Compact space|compact]] (closed and bounded) fixed set ''S''.

{{r|Compact space}}

; Compactness: {{Main|Compactness axioms}}<math>X</math> is said to be ''[[Compact space|compact]]'' if any open cover of <math>X</math> has a ''finite sub-cover''.

...infin; are added to the reals to form the [[extended real number line]], a compact space which is not a field but retains many of the properties of the real numbers

* [[compact space]]s (and compact Hausdorff spaces, i.e. compact <math>\ T_2</math>-spaces);

During this period, a method of manufacturing many transistors in a compact space gained popularity. The [[integrated circuit]] ('''IC''') allowed a large n