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Tatra Mountains Mathematical Publications, ISSN 1210-3195, 12/2018, Volume 72, Issue 1, pp. 55 - 66
In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define -bounded... 
continuity | 54C30 | aggregation function | super-additive transformation | 28E10
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 02/2020, Volume 70, Issue 1, pp. 183 - 192
Considering the natural topology or 𝓢-density topology on the domain and on the range we obtain different families of continuous functions : ℝ → ℝ. In this... 
54A10 | 54C30 | density-types topologies | approximately continuous functions | 54C35 | porosity | function spaces | continuity | 26A15 | 54C08
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2019, Volume 26, Issue 4, pp. 643 - 654
We consider some families of real functions endowed with the metric of uniform convergence. In the main results of our work we present two methods of... 
strong porosity | comparison of families of real functions | 54C30 | path continuity | Porosity | 54C50 | 54C08 | MATHEMATICS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 02/2019, Volume 69, Issue 1, pp. 199 - 212
The notion of porouscontinuity was introduced by Borsík and Holos. We find classes of functions whose compositions with porouscontinuous functions are still... 
homeomorphism | porosity | Primary 54C30 | porouscontinuity | real valued functions | 26A15 | compositions | 54C08 | MATHEMATICS | Composition
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 449 - 452
We find non-regular Hausdorff -spaces (connected or not). We also prove that a countable Hausdorff connected space cannot be an -space. 
connected | Primary 54D10 | countable connected | extremally disconnected | 54D05 | Secondary 54C30 | 54G05 | MATHEMATICS
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 01/2017, Volume 40, Issue 1, pp. 63 - 73
Let A(X) be an intermediate subring of C(X) and I be an ideal of A(X). We give some topological characterizations for the smallest z-ideal I z (A) containing I... 
46E25 | 54C30 | intermediate C-algebra | realcompactification | Maximal growing ideal
Journal Article
Algebra universalis, ISSN 0002-5240, 12/2019, Volume 80, Issue 4, pp. 1 - 14
Let C(X) denote the ring of all real-valued continuous functions on a topological space X and $${\mathcal {R}} (L)$$ R(L) be as the pointfree topology version... 
Ring of real-valued continuous functions | 54C30 | Algebra | 06D22 | Compact frame | Connected frame | Mathematics | 54C05 | Countable image | Zero-dimensional frame
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 12/2018, Volume 68, Issue 6, pp. 1465 - 1476
Limit numbers (cluster sets) of a real function of a real variable were discussed in the literature by many authors. Generalizations of cluster sets were... 
limit numbers | topology generated by limit numbers | generalized limit numbers | Primary 54C30 | MATHEMATICS
Journal Article
Journal of Applied Analysis, ISSN 1425-6908, 12/2016, Volume 22, Issue 2, pp. 141 - 151
In the present paper, we introduce the notion of symmetrically porouscontinuous functions. We investigate some properties of symmetric porouscontinuity and its... 
54C30 | symmetric porouscontinuity | porouscontinuity | symmetric porosity | Porosity | 26A15 | 54C08
Journal Article
Tatra Mountains Mathematical Publications, ISSN 1210-3195, 03/2017, Volume 68, Issue 1, pp. 13 - 28
In the present paper, we introduce notions of v-porosity and v-porouscontinuity. We investigate some properties of v-poroucontinuity and its connections with... 
54C30 | porosity | v-porouscontinuity | porouscontinuity | 26A15 | v-porosity | 54C08
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 10/2019, Volume 42, Issue 9, pp. 1141 - 1157
Let C(X) denote the ring of all real-valued continuous functions on a topological space X; and C ∞ (X) be the subring of all functions C(X) which vanish at... 
54C30 | Frame | 06D22 | continuous frame | vanish at infinity | 54C05 | locally compact space
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2019, Volume 26, Issue 4, pp. 573 - 582
In the first part of the paper we study the sets of boundedness and of convergence and divergence to infinity of sequences of real closed-graph functions.... 
40A30 | 54C30 | Ideal convergence | functions with closed graphs | 40A35 | 26A21 | MATHEMATICS | J-universal set | F-sigma-ideal | omega-diagonalizability
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 469 - 473
It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are -embedded. In particular, this generalizes the... 
54C30 | isolated points | 54A25 | essential ideals | spaces | socle | 54D60 | embedded | realcompact spaces | P | C-embedded | MATHEMATICS | P-lambda-spaces
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 4/2019, Volume 157, Issue 2, pp. 459 - 464
For a Tychonoff space X, we will denote by USC p (X) (B 1(X)) the set of all real-valued upper semicontinuous functions (the set of all Baire functions of... 
54C30 | 54A20 | 54C35 | continuous function | upper semicontinuous function | sequentially separable | Mathematics, general | Mathematics | function space | 54H05 | Baire function of class 1 | MATHEMATICS
Journal Article
Algebra universalis, ISSN 0002-5240, 3/2018, Volume 79, Issue 1, pp. 1 - 14
In classical topology, it is proved that for a topological space X, every bounded Riesz map $$\varphi :C (X) \rightarrow {\mathbb {R}}$$ φ:C(X)→R is of the... 
54C30 | Frame | Algebra | 06D22 | Dedekind cut | 13A15 | Mathematics | Lattice-valued map | Strong f-ring | MATHEMATICS
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 08/2017, Volume 40, Issue 5, pp. 623 - 626
In this paper we characterize the pairs (A − , A + ) of disjoint subsets of a perfectly normal topological space which can be separated by a function with a... 
54C30 | Secondary 26A15 | Primary 26A21 | Urysohn lemma | separating sets | 54C08 | Functions with a closed graph | MATHEMATICS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 10/2019, Volume 69, Issue 5, pp. 999 - 1008
Let 𝓕 := Frm(𝓟(ℝ), ). We show that if is a -frame then 𝓕 is an ℵ -self-injective ring. We prove that a zero-dimensional frame is extremally disconnected if... 
regular ring | 54C30 | 06D22 | zero-dimensional frame | 16D50 | extremally disconnected frame | Baer ring | 54C05 | injective ring | 54G05 | frame | MATHEMATICS | P-frame
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 885 - 905
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2017, Volume 14, Issue 2, pp. 1 - 7
In this paper, we prove that the density of the topology of uniform convergence d(C(X)) is equal to the density of the m-topology. For general topological... 
54C30 | Cardinal invariant | 54C35 | 54A25 | m -topology | Mathematics, general | Mathematics | topology of uniform convergence
Journal Article
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