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* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.

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Wikipedia

## Some Related Sentences

Every and totally

** Zorn's lemma:

__Every__non-empty partially ordered set in which every chain ( i**.**e**.**__totally__ordered**subset**) has an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered set has**a**maximal__totally__ordered**subset**"**is**also equivalent**to**AC over ZF**.*******

__Every__

__totally__ordered set that

**is**

**a**bounded lattice

**is**also

**a**Heyting algebra, where

**is**equal

**to**when, and 1 otherwise

**.**

__Every__November the Reebok Stadium hosts Kidz up North which

**is**one

**of**the largest free UK exhibitions

__totally__dedicated

**to**children with disabilities and special needs, their parents, carers and professionals who work with them

**.**

__Every__

**subset**

**of**

**a**

__totally__bounded

**space**

**is**

**a**

__totally__bounded set ; but even if

**a**

**space**

**is**not

__totally__bounded, some

**of**its subsets still will be

**.**

Every and compact

*****

__Every__topological

**space**X

**is**

**a**dense subspace

**of**

**a**

__compact__

**space**having at most one point more than X, by the Alexandroff one-point compactification

**.**

*****

__Every__continuous map from

**a**

__compact__

**space**

**to**

**a**Hausdorff

**space**

**is**closed and proper ( i

**.**e., the pre-image

**of**

**a**

__compact__set

**is**

__compact__

**.**

__Every__entire function can be represented as

**a**power series that converges uniformly on

__compact__sets

**.**

*****

__Every__locally

__compact__regular

**space**

**is**completely regular, and therefore every locally

__compact__Hausdorff

**space**

**is**Tychonoff

**.**

__Every__

__compact__Hausdorff

**space**

**is**also locally

__compact__, and many examples

**of**

__compact__

**spaces**may be found in the article

__compact__

**space**

**.**

*****

__Every__

__compact__Hausdorff

**space**

**of**weight at most ( see Aleph number )

**is**the continuous image

**of**( this does not need the continuum hypothesis, but

**is**less interesting in its absence ).

__Every__group has

**a**presentation, and in fact many different presentations ;

**a**presentation

**is**often the most

__compact__way

**of**describing the structure

**of**the group

**.**

__Every__H

*****

**is**very special in structure: it

**is**pure-injective ( also called algebraically

__compact__), which says more or less that solving equations in H

*****

**is**relatively straightforward

**.**

Every and metric

*****

__Every__separable

__metric__

**space**

**is**isometric

**to**

**a**

**subset**

**of**the ( non-separable ) Banach

**space**l < sup >∞</ sup >

**of**all bounded real sequences with the supremum norm ; this

**is**known as the Fréchet embedding

**.**

*****

__Every__separable

__metric__

**space**

**is**isometric

**to**

**a**

**subset**

**of**C (), the separable Banach

**space**

**of**continuous functions → R, with the supremum norm

**.**

__Every__smooth submanifold

**of**R < sup > n </ sup > has an induced Riemannian

__metric__g: the inner

**product**on each tangent

**space**

**is**the restriction

**of**the inner

**product**on R < sup > n </ sup >.

__Every__building has

**a**canonical length

__metric__inherited from the geometric realisation obtained by identifying the vertices with an orthonormal basis

**of**

**a**Hilbert

**space**

**.**

This

**is**really**a**special case**of****a**more general fact:__Every__continuous function from**a****compact****space**into**a**__metric__**space****is**bounded**.**
#

__Every__Riemannian__metric__on**a**Riemann surface**is**Kähler, since the condition for ω**to**be closed**is**trivial in 2 ( real ) dimensions**.**__Every__hyperkähler manifold M has

**a**2-sphere

**of**complex structures ( i

**.**e

**.**integrable almost complex structures ) with respect

**to**which the

__metric__

**is**Kähler

**.**

__Every__special uniformly continuous real-valued function defined on the

__metric__

**space**

**is**uniformly approximable by means

**of**Lipschitz functions

**.**

__Every__

__metric__

**space**which

**is**ccc

**is**also separable, but in general

**a**ccc topological

**space**need not be separable

**.**

__Every__locally

**compact**group which

**is**second-countable

**is**metrizable as

**a**topological group ( i

**.**e

**.**can be given

**a**left-invariant

__metric__compatible with the topology ) and complete

**.**

1.532 seconds.