Öz
Let $R$ be a topological ring and $E$, $F$ be unitary topological $R$-modules. Denote by $C_p(X,E)$ the class of all continuous mappings of $X$ into $E$ in the topology of pointwise convergence. The spaces $X$ and $Y$ are called $l_p(E,F)$-equivalent if the topological $R$-modules $C_p(X,E)$ and $C_p(Y,F)$ are topological isomorphic. Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.
Anahtar Kelimeler
Function space topology of pointwise convergence support linear homeomorphism perfect properties open finite-to-one properties
Kaynakça
- A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992.
- A. V. Arhangel'skii, On linear homomorphisms of function spaces, Doklady Acad. Nauk SSSR 264 (1982), no. 6, 1289-1292. English translation: Soviet Math. Dokl. 25 (1982), 852-855.
- M.M. Choban, General theorems on functional equivalence of topological spaces, Topology Appl. 89 (1998), 223-239.
- M.M. Choban, Algebraical equivalence of topological spaces, Buletinul Acad. de tiinµe a Republicii Moldova, Matematica, 1 (2001), 12-36.
- M. Choban, Open finite-to-one mappings, Soviet Math. Dokl. 8 (1967), 603-603.
- M.M. Choban, On the theory of topological algebraic systems, Trudy Moskovskogo Matem. Obshchestva 48 (1985), 106-149. English translation: Trans. Moscow Math. Soc. 48, 1986, 115-159.
- M.M. Choban, Some topics in topological algebra, Topology Appl. 54 (1993), 183-202.
- M.M. Choban, R. N. Dumbraveanu, $l_p(R)$-equivalence of topological spaces and topological modules, Buletinul Academiei de Stiinte a Rep. Moldova, Matematica 1 (2015), 20-47.
- R. Engelking, General Topology, PWN, Warsawa 1977.
- J. S. Golan, Semirings and their applications, Springer, 1999.
- V. P. Maslov, Idempotent analysis, American Mathematical Society, 1992.
- J. van Mill, The in finite-dimensional topology of function spaces, North-Holland Mathemat- ical Library, Amsterdam, vol. 64, 2001.
- A. Okuyama, A survey of the theory of $\sigma$-spaces, General Topology Appl. 1 (1971), 57-63.
- V. Valov, Function spaces, Topology Appl. 81 (1997), no. 1, 1-22.
- S. Warner, Topological rings, North-Holland mathematics studies. Elsevier, v. 178, 1993.
Öz
Kaynakça
- A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992.
- A. V. Arhangel'skii, On linear homomorphisms of function spaces, Doklady Acad. Nauk SSSR 264 (1982), no. 6, 1289-1292. English translation: Soviet Math. Dokl. 25 (1982), 852-855.
- M.M. Choban, General theorems on functional equivalence of topological spaces, Topology Appl. 89 (1998), 223-239.
- M.M. Choban, Algebraical equivalence of topological spaces, Buletinul Acad. de tiinµe a Republicii Moldova, Matematica, 1 (2001), 12-36.
- M. Choban, Open finite-to-one mappings, Soviet Math. Dokl. 8 (1967), 603-603.
- M.M. Choban, On the theory of topological algebraic systems, Trudy Moskovskogo Matem. Obshchestva 48 (1985), 106-149. English translation: Trans. Moscow Math. Soc. 48, 1986, 115-159.
- M.M. Choban, Some topics in topological algebra, Topology Appl. 54 (1993), 183-202.
- M.M. Choban, R. N. Dumbraveanu, $l_p(R)$-equivalence of topological spaces and topological modules, Buletinul Academiei de Stiinte a Rep. Moldova, Matematica 1 (2015), 20-47.
- R. Engelking, General Topology, PWN, Warsawa 1977.
- J. S. Golan, Semirings and their applications, Springer, 1999.
- V. P. Maslov, Idempotent analysis, American Mathematical Society, 1992.
- J. van Mill, The in finite-dimensional topology of function spaces, North-Holland Mathemat- ical Library, Amsterdam, vol. 64, 2001.
- A. Okuyama, A survey of the theory of $\sigma$-spaces, General Topology Appl. 1 (1971), 57-63.
- V. Valov, Function spaces, Topology Appl. 81 (1997), no. 1, 1-22.
- S. Warner, Topological rings, North-Holland mathematics studies. Elsevier, v. 178, 1993.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Şubat 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 46 Sayı: 1 |