Abstract
AbstractIn the paper we study properties of a lower porosity of a set in a normed space $$(X,\Vert \;\Vert )$$
(
X
,
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‖
)
. Two topologies $${\underline{p}}(X,\Vert \;\Vert )$$
p
̲
(
X
,
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)
and $${\underline{s}}(X,\Vert \;\Vert )$$
s
̲
(
X
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)
on X generated by the lower porosity are defined. Relationships between these topologies and, previously defined by V. Kelar and L. Zajíček, topologies $$p(X,\Vert \;\Vert )$$
p
(
X
,
‖
‖
)
and $$s(X,\Vert \;\Vert )$$
s
(
X
,
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)
are studied. Applying topologies $${\underline{p}}(X,\Vert \;\Vert )$$
p
̲
(
X
,
‖
‖
)
and $${\underline{s}}(X,\Vert \;\Vert )$$
s
̲
(
X
,
‖
‖
)
we characterize maximal additive class of lower porouscontinuous functions. Some relevant properties of defined topologies are considered.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference13 articles.
1. Borsík, J., Holos, J.: Some properties of porouscontinuous functions. Math. Slovaca 64(3), 741–750 (2014)
2. Borsík, J., Kowalczyk, S., Turowska, M.: On points of porouscontinuity. Topol. Appl. 284, 107410 (2020)
3. Bruckner, A.M.: Differentation of Real Functions. Lecture Notes in Mathematics, vol. 659. Springer-Verlag, Berlin (1978)
4. Dolženko, E.P.: Boundary properties of arbitrary functions. Math. USSR Izv. 31, 3–14 (1967)
5. Filipczak, M., Ivanova, G., Wódka, J.: Comparison of some families of real functions in porosity terms. Math. Slovaca 67, 1155–1164 (2017)