Tychonoff space

A topological space $X$ is said to be completely regular if whenever $C\\subseteq X$ is closed and $x\\in X\\setminus C$ then there is a continuous function $f\\colon X\\to[0,1]$ with $f(x)=0$ and $f(C)\\subseteq\\{1\\}$ .

A completely regular space that is also $T_{0}$ (http://planetmath.org/T0Space) (and therefore Hausdorff (http://planetmath.org/T2Space))is called a Tychonoff space, or a $T_{3\\frac{1}{2}}$ space.

Some authors interchange the meanings of ‘completely regular’ and ‘ $T_{3\\frac{1}{2}}$ ’ compared to the above.

It can be proved that a topological space is Tychonoffif and only if it has a Hausdorff compactification.

单词	TychonoffSpace
释义	Tychonoff space A topological space $X$ is said to be completely regular if whenever $C\\subseteq X$ is closed and $x\\in X\\setminus C$ then there is a continuous function $f\\colon X\\to[0,1]$ with $f(x)=0$ and $f(C)\\subseteq\\{1\\}$ . A completely regular space that is also $T_{0}$ (http://planetmath.org/T0Space) (and therefore Hausdorff (http://planetmath.org/T2Space))is called a Tychonoff space, or a $T_{3\\frac{1}{2}}$ space. Some authors interchange the meanings of ‘completely regular’ and ‘ $T_{3\\frac{1}{2}}$ ’ compared to the above. It can be proved that a topological space is Tychonoffif and only if it has a Hausdorff compactification.
随便看	tautologies in predicate logic Tautology tautology TaxicabNumbers taxicab numbers TaylorExpansionOfsqrt1x Taylor expansion of sqrt(1+x) TaylorFormulaRemainderVariousExpressions Taylor formula remainder: various expressions TaylorSeries Taylor series TaylorSeriesDerivationOf Taylor series, derivation of TaylorSeriesOfArcusSine Taylor series of arcus sine TaylorSeriesOfArcusTangent Taylor series of arcus tangent TaylorSeriesOfHyperbolicFunctions Taylor series of hyperbolic functions TaylorSeriesViaDivision Taylor series via division TaylorsFormulaForMatrixFunctions TaylorsFormulaInBanachSpaces TaylorsTheorem Taylor’s formula for matrix functions