THE PACKING DIMENSION OF A TYPICAL CONTINUOUS FUNCTION IS 2

1988 ◽  
Vol 14 (2) ◽  
pp. 345 ◽  
Author(s):  
Humke ◽  
Petruska
Keyword(s):  
Continuous Function ◽  
Packing Dimension ◽  
Typical Continuous Function

The packing measure of the graphs and level sets of certain continuous functions

1988 ◽  
Vol 104 (2) ◽  
pp. 347-360 ◽  
Author(s):  
Fraydoun Rezakhanlou
Keyword(s):  
Continuous Function ◽  
Level Sets ◽  
Continuous Functions ◽  
Packing Dimension ◽  
Packing Measure ◽  
Occupation Measure ◽  
Weierstrass Function ◽  
Local Growth ◽  
Almost All ◽  
The Relationship

AbstractThe relationship between the local growth of a continuous function and the packing measure of its level sets and of its graph is studied. For the Weierstrass function with b an integer such that b ≥ 2 and with 0 < α < 1, and for x ∈ Range (W) outside a set of first category, the level set W−1(x) has packing dimension at least 1 − α. Furthermore, for almost all x ∈ Range (W), the packing dimension of f is at most 1 − α. Finer results on the occupation measure and the size of the graph of a continuous function satisfying the Zygmund Λ-condition are obtained.

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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