Wyniki wyszukiwania

1

Large free set

100%

Muthuvel K.

Colloquium Mathematicum

|

1992

|

tom 63

|

nr 1

107-109

2

Application of covering sets

100%

Muthuvel K.

Colloquium Mathematicum

|

1999

|

tom 80

|

nr 1

115-122

3

On nowhere weakly symmetric functions and functions with two-element range

51%

Ciesielski K., Muthuvel K., Nowik A.

Fundamenta Mathematicae

|

2001

|

tom 168

|

nr 2

119-130

EN

A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each point x we ignore some countable set from which we can choose the sequence hₙ, then there exists a function f: ℝ → {0,1} which is nowhere weakly symmetric in this weaker sense if and only if the continuum hypothesis holds.

4

Infinite products of alephs

32%

Muthuvel K.

Fundamenta Mathematicae

|

1988

|

tom 131

|

nr 3

255-256

Ograniczanie wyników

2 Colloquium Mathematicum

2 Fundamenta Mathematicae

4 Muthuvel K.

1 Ciesielski K.

1 Nowik A.

1 2001

1 1999

1 1992

1 1988

Large free set

Application of covering sets

On nowhere weakly symmetric functions and functions with two-element range

Infinite products of alephs