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Extending continuous functions defined on subsets of products
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Extending continuous functions defined on subsets of products
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Description
Identifier
Thesis
2195
Author
Rivers, Douglas Michael, 1984
Title
Extending
continuous
functions
defined
on
subsets
of
products
Publisher
Central Connecticut State University
Date of Publication
2011
Resource Type
Master's Thesis
Abstract
Let
X
and
Z
be
topological
spaces
and
Y
be a
subspace
of
X
. A
con
tinuous
function
f
:
Y
!
Z
is
extendable
to
X
if there
exists
a
continuous
function
f
:
X
!
Z
such
that
f(x)
=
f(x)
for
all
x
2
Y
. If
every
continuous
function
f
:
Y
!
Z
is
extendable
to
X
then
Y
is
called
C(Z)embedded
in
X
.
According
to
R
.
Engelking
,
\theorems
that
give
su
cient
conditions
for
extendability
of
continuous
mappings
of
continuous
realvalued
functions
are
among
the
most
important
ones
in
topology
, and
usually
are
rather
di
cult.
" In this
thesis
we
analyze
three
such
theorems
by
Milton
Ulmer
that
ap
peared
in his
paper
Cembedded
spaces
,
Paci
c
J
.
Math
,
46
(1973)
,
591{
602
, and
some
results
generalizing
two
of the
Ulmer's
theorems
that
appeared
recently
in
two
papers
by
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
:
Continuous
Mappings
on
Subspaces
of
Products
with the
box
Topology
,
Topology
Appl
.
156
(2009)
,
No
.
16
,
2600{2608
and
Continuous
Extensions
of
Functions
De
ned
on
Subsets
of
Products
,
accepted
for
publication
in
Topology
Appl
.
After
that
we
formulate
and
prove
a
theorem
that
signi
cantly
generalizes
two
of the
Ulmer's
theorems
and a
theorem
by
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
. This
contribution
to the
topic
is
a
joint
work
with
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
.
Subject
Topology
Topological spaces
Department
Department of Mathematical Sciences
Advisor
Gotchev, Ivan S.
Type
Text
Digital Format
application/pdf
Language
eng
OCLC number
804653037
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