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Title
Comonotone approximation and interpolation by entire functions
Source
Journal of Mathematical Analysis and Applications
Date
2019
Author
Burke, Maxim R.
Genre
Journal Article
Volume
480
Issue
2
Start Page
123427
DOI
10.1016/j.jmaa.2019.123427
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Title
Approximation by entire functions in the construction of order-isomorphisms and large cross-sections
Source
New trends in approximation theory
Date
2018
Author
Burke, Maxim R.
Genre
Book, Section
Start Page
37
ISBN
978-1-4939-7543-3
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Title
Approximation and interpolation by entire functions with restriction of the values of the derivatives
Source
Topology and its Applications
Date
2016
Author
Burke, Maxim R.
Genre
Journal Article
Volume
213
Start Page
24
DOI
10.1016/j.topol.2016.08.005
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Title
Approximation and interpolation by large entire cross-sections of second category sets in Rn+1
Source
Topology and its Applications
Date
2013
Author
Burke, Maxim R.
Genre
Journal Article
Abstract
In [M.R. Burke, Large entire cross-sections of second category sets in Rn+1Rn+1, Topology Appl. 154 (2007) 215–240], a model was constructed in...
Volume
160
Issue
3
Start Page
1681
DOI
10.1016/j.topol.2013.07.003
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Title
Various products of category densities and liftings
Source
Topology and its Applications
Date
2009
Author
Burke, M. R.
;
Macheras, N. D.
;
Musiał, K.
;
Strauss, W.
Genre
Journal Article
Volume
156
Issue
7
Start Page
1253
DOI
10.1016/j.topol.2008.12.002
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Title
Entire functions mapping uncountable dense sets of reals onto each other monotonically
Source
Transactions of the American Mathematical Society
Date
2009
Author
Burke, Maxim R.
Genre
Journal Article
Volume
361
Issue
6
Start Page
2871
DOI
10.1090/S0002-9947-09-04924-1
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Title
Simultaneous approximation and interpolation of increasing functions by increasing entire functions
Source
Journal of Mathematical Analysis and Applications
Date
2009
Author
Burke, Maxim R.
Genre
Journal Article
Volume
350
Issue
2
Start Page
845
DOI
10.1016/j.jmaa.2008.08.018
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Title
Large entire cross-sections of second category sets in Rn+1
Source
Topology and its Applications
Date
2007
Author
Burke, Maxim R.
Genre
Journal Article
Abstract
By the Kuratowski-Ulam theorem, if A subset of Rn+1 = R-n x R is a Borel set which has second category intersection with every ball (i.e., is ...
Volume
154
Issue
1
Start Page
215
DOI
10.1016/j.topol.2006.04.009
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Title
Category product densities and liftings
Source
Topology and its Applications
Date
2006
Author
Burke, Maxim R.
;
Macheras, N. D.
;
Musial, K.
;
Strauss, W.
Genre
Journal Article
Abstract
In this paper we investigate two main problems. One of them is the question on the existence of category liftings in the product of two topological...
Volume
153
Issue
7
Start Page
1164
DOI
10.1016/j.topol.2004.12.008
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Title
Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set
Source
Canadian Journal of Mathematics / Journal Canadien De Mathematiques
Date
2005
Author
Burke, Maxim R.
;
Miller, A. W.
Genre
Journal Article
Abstract
We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor...
Volume
57
Issue
6
Start Page
1139
DOI
10.4153/cjm-2005-044-x
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Title
Hechler’s theorem for the null ideal
Source
Archive for Mathematical Logic
Date
2004
Author
Burke, Maxim R.
;
Kada, Masaru
Genre
Journal Article
Volume
43
Issue
5
Start Page
703
DOI
10.1007/s00153-004-0224-4
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Title
Paradoxical decompositions of planar sets of positive outer measure Paradoxical decompositions of planar sets
Source
Journal of Geometry
Date
2004
Author
Burke, Maxim R.
Genre
Journal Article
Volume
79
Issue
1
Start Page
56
DOI
10.1007/s00022-003-1575-4
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Title
Borel measurability of separately continuous functions, II
Source
Topology and its Applications
Date
2003
Author
Burke, Maxim R.
Genre
Journal Article
Abstract
This paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29-65] into the measurability properties of separately...
Volume
134
Issue
3
Start Page
159
DOI
10.1016/S0166-8641(03)00105-6
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Title
[Review of the book Introduction to Cardinal Arithmetic by M. Holz, K. Steffens, and E. Weitz]
Source
The Bulletin of Symbolic Logic
Date
2002
Author
Burke, Maxim R.
Genre
Journal Article
Volume
8
Issue
4
Start Page
524
DOI
10.2307/797958
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Title
Continuous functions which take a somewhere dense set of values on every open set (vol 103, pg 95, 2000)--correction
Source
Topology and its Applications
Date
2000
Author
Burke, Maxim R.
Genre
Journal Article
Volume
108
Issue
1
Start Page
105
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Title
Continuous functions which take a somewhere dense set of values on every open set
Source
Topology and its Applications
Date
2000
Author
Burke, Maxim R.
Genre
Journal Article
Abstract
We study the class of Tychonoff spaces that can be mapped continuously into R in such a way that the preimage of every nowhere dense set is nowhere...
Volume
103
Issue
1
Start Page
95
DOI
10.1016/S0166-8641(98)00163-1
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Title
Sets of range uniqueness for classes of continuous functions
Source
Proceedings of the American Mathematical Society
Date
1999
Author
Burke, Maxim R.
;
Ciesielski, K.
Genre
Journal Article
Abstract
Diamond, Pomerance and Rubel (1981) proved that there are subsets M of the complex plane such that for any two entire functions f and g if f[M] = g...
Volume
127
Issue
11
Start Page
3295
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Title
Sets on which measurable functions are determined by their range
Source
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
Date
1997
Author
Burke, Maxim R.
;
Ciesielski, K.
Genre
Journal Article
Abstract
We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.
Volume
49
Issue
6
Start Page
1089
DOI
10.4153/cjm-1997-054-8
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Title
A proof of Hechler's theorem on embedding N-1-directed sets cofinally into ((ωω, <∗)
Source
Archive for Mathematical Logic
Date
1997
Author
Burke, Maxim R.
Genre
Journal Article
Abstract
We give a proof of Hechler's theorem that any aleph(1)-directed partial order can be embedded via a ccc forcing notion cofinally into omega(omega)...
Volume
36
Issue
6
Start Page
399
DOI
10.1007/s001530050072
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Title
Bounded sets in topological vector spaces
Source
Mathematische Annalen
Date
1996
Author
Burke, Maxim R.
;
Todorcevic, S.
Genre
Journal Article
Volume
305
Issue
1
Start Page
103
DOI
10.1007/bf01444213
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1
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