THE STRUCTURE OF THE SETS {X: f(x) = h(x)} FOR A TYPICAL CONTINUOUS FUNCTION f AND FOR A CLASS OF LIPSCHITZ FUNCTIONS h

1981 ◽  
Vol 7 (2) ◽  
pp. 271
Author(s):  
Wójtowicz
Keyword(s):  
Continuous Function ◽  
Lipschitz Functions ◽  
Typical Continuous Function

scholarly journals Lipschitz one sets modulo sets of measure zero

2020 ◽  
Vol 70 (3) ◽  
pp. 567-584 ◽  
Author(s):  
Zoltán Buczolich ◽  
Bruce Hanson ◽  
Balázs Maga ◽  
Gáspár Vértesy
Keyword(s):  
Continuous Function ◽  
Lebesgue Measure ◽  
Measure Zero ◽  
Lipschitz Functions ◽  
The Other ◽  
Uniform Density ◽  
Other Hand ◽  
Measurable Set

AbstractWe denote the local “little” and “big” Lipschitz functions of a function f : ℝ → ℝ by lip f and Lip f. In this paper we continue our research concerning the following question. Given a set E ⊂ ℝ is it possible to find a continuous function f such that lip f = 1E or Lip f = 1E?In giving some partial answers to this question uniform density type (UDT) and strong uniform density type (SUDT) sets play an important role.In this paper we show that modulo sets of zero Lebesgue measure any measurable set coincides with a Lip 1 set.On the other hand, we prove that there exists a measurable SUDT set E such that for any Gδ set E͠ satisfying ∣EΔE͠∣ = 0 the set E͠ does not have UDT. Combining these two results we obtain that there exist Lip 1 sets not having UDT, that is, the converse of one of our earlier results does not hold.

Generalized ʎ-Closed Sets and (ʎ-ʏ)*-Continuous Function

2017 ◽  
Vol 4 (ICBS Conference) ◽  
pp. 1-17 ◽  
Author(s):  
Alias Khalaf ◽  
Sarhad Nami
Keyword(s):  
Continuous Function ◽  
Closed Sets

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Limit of Simply Continuous Function

1992 ◽  
Vol 18 (1) ◽  
pp. 270 ◽  
Author(s):  
Borsík
Keyword(s):  
Continuous Function
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