Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Products of Michael spaces and completely metrizable spaces
View through CrossRef
For disjoint subsets
A
,
C
A,C
of
[
0
,
1
]
[0,1]
the Michael space
M
(
A
,
C
)
=
A
∪
C
M(A,C)=A\cup C
has the topology obtained by isolating the points in
C
C
and letting the points in
A
A
retain the neighborhoods inherited from
[
0
,
1
]
[0,1]
. We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a Lindelöf Michael space
M
(
A
,
C
)
M(A,C)
, of minimal weight
ℵ
1
\aleph _1
, with
M
(
A
,
C
)
×
B
(
ℵ
0
)
M(A,C)\times B(\aleph _0)
Lindelöf but with
M
(
A
,
C
)
×
B
(
ℵ
1
)
M(A,C)\times B(\aleph _1)
not normal. (
B
(
ℵ
α
)
B(\aleph _\alpha )
denotes the countable product of a discrete space of cardinality
ℵ
α
\aleph _\alpha
.) If
M
(
A
)
M(A)
denotes
M
(
A
,
[
0
,
1
]
∖
A
)
M(A,[0,1]\smallsetminus A)
, the normality of
M
(
A
)
×
B
(
ℵ
0
)
M(A)\times B(\aleph _0)
implies the normality of
M
(
A
)
×
S
M(A)\times S
for any complete metric space
S
S
(of arbitrary weight). However, the statement “
M
(
A
,
C
)
×
B
(
ℵ
1
)
M(A,C)\times B(\aleph _1)
normal implies
M
(
A
,
C
)
×
B
(
ℵ
2
)
M(A,C)\times B(\aleph _2)
normal” is axiom sensitive.
American Mathematical Society (AMS)
Title: Products of Michael spaces and completely metrizable spaces
Description:
For disjoint subsets
A
,
C
A,C
of
[
0
,
1
]
[0,1]
the Michael space
M
(
A
,
C
)
=
A
∪
C
M(A,C)=A\cup C
has the topology obtained by isolating the points in
C
C
and letting the points in
A
A
retain the neighborhoods inherited from
[
0
,
1
]
[0,1]
.
We study normality of the product of Michael spaces with complete metric spaces.
There is a ZFC example of a Lindelöf Michael space
M
(
A
,
C
)
M(A,C)
, of minimal weight
ℵ
1
\aleph _1
, with
M
(
A
,
C
)
×
B
(
ℵ
0
)
M(A,C)\times B(\aleph _0)
Lindelöf but with
M
(
A
,
C
)
×
B
(
ℵ
1
)
M(A,C)\times B(\aleph _1)
not normal.
(
B
(
ℵ
α
)
B(\aleph _\alpha )
denotes the countable product of a discrete space of cardinality
ℵ
α
\aleph _\alpha
.
) If
M
(
A
)
M(A)
denotes
M
(
A
,
[
0
,
1
]
∖
A
)
M(A,[0,1]\smallsetminus A)
, the normality of
M
(
A
)
×
B
(
ℵ
0
)
M(A)\times B(\aleph _0)
implies the normality of
M
(
A
)
×
S
M(A)\times S
for any complete metric space
S
S
(of arbitrary weight).
However, the statement “
M
(
A
,
C
)
×
B
(
ℵ
1
)
M(A,C)\times B(\aleph _1)
normal implies
M
(
A
,
C
)
×
B
(
ℵ
2
)
M(A,C)\times B(\aleph _2)
normal” is axiom sensitive.
Related Results
Buy Psychedelic Products Online (Preprint)
Buy Psychedelic Products Online (Preprint)
BACKGROUND
Contact +1 (601) 721-8695
Email sales@psychdistro.com
Address 7777 W 38th Ave A104 Wheat Ridge CO 80033 United States
Looking for the highest-...
Some Progress on the Unique Ergodicity Problem
Some Progress on the Unique Ergodicity Problem
AbstractThis thesis is at the intersection of dynamics, probability and model theory. It focuses on a specialization of the notion of amenability: unique ergodicity.Let G be a Poli...
DIEUDONN ÉCOMPLETE BISPACES
DIEUDONN ÉCOMPLETE BISPACES
A bispace is called Dieudonn ´e complete if it admits a compatible bicomplete quasi- uniformity.We characterize pairwise Tychono .Dieudonn ´e complete bispaces in terms of their si...
τ-metrizable spaces
τ-metrizable spaces
<p>In [1], A. A. Borubaev introduced the concept of τ-metric space, where τ is an arbitrary cardinal number. The class of τ-metric spaces as τ runs through the cardinal numbe...
EKSISTENSI MANTAN PETINJU NASIONAL SEBAGAI PETARUNG PENCAK DOR KEDIRI MELALUI FILM DOKUMENTER POTRET “MICHAEL SPEED”
EKSISTENSI MANTAN PETINJU NASIONAL SEBAGAI PETARUNG PENCAK DOR KEDIRI MELALUI FILM DOKUMENTER POTRET “MICHAEL SPEED”
ABSTRAKPenyutradaraan karya film dokumenter potret ini ialah untuk memberikan gambaran kehidupan seorang mantan petinju nasional dan petarung Pencak Dor di Kediri bernama Michael ‘...
Concerning Fuzzy b-Metric Spaces †
Concerning Fuzzy b-Metric Spaces †
In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Năd...
COUNTABLE SPACES WITH PEANO PROPERTY
COUNTABLE SPACES WITH PEANO PROPERTY
In 1890, Giuseppe Peano published an example of a continuous curve passing through every point of the square $[0,1]^2$. A curve with such properties is called a Peano curve. In fa...
Engineering Applicability of a Universal Design Performance Measure
Engineering Applicability of a Universal Design Performance Measure
Universal Design (UD) is defined as the creation of products and environments to be usable by all people, to the greatest extent possible, without the need for adaptation or specia...