A note on p-bounded and quasi-p-bounded subsets

Houston Journal of Mathematics

Volumn 28, Issue 3, 2002, Pages 511-527

  Sanchis, Manuel ^a   Tamariz Mascarúa, Angel ^b  

^a UNIVERSITAT JAUME I   (Spain)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

b discrete space; C compact set; Generalized Linearly Topological Spaces; p bounded set; p compact space; p limit point; p pseudocompact space; P space; Quasi p bounded set; Spaces of continuous functions; Strongly bounded set; Topological group

Indexed keywords

EID: 0037653471     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. A.R. Bernstein, A new kind of compactness for topological spaces, Fund. Math. 66 (1970), 185-193.
2. N. Bourbaki, Éléments de Mathématiques, Chap. 1-4, Hermann, Paris, 1971.
3. f-spaces, Acta Math. Hung. 62, No. 1-2, (1993), 111-118.
4. R. Engelking, General Topology, Polish Scientific Publishers, Warzawa, 1977.
5. R. Fox, A note on topological groups with dense orderable subspaces, Topology and Order Structures II, Math. Centre Tracts 169, Amsterdam, 1983, 37-38.
6. Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc., 73, (1967), 87-91.
7. S. García-Ferreira, Some Generalizations of pseudocompactness, Annals New York Academy of Sciences, 728, (1994), 22-31.
8. S. García-Ferreira, Quasi M-compact spaces, Czech. Math. J. 46, (1996), 161-177.
9. S. García-Ferreira and A. García-Máynez, On weakly-pseudocompact spaces, Houston J. Math. 20, (1994), 145-159.
10. S. García-Ferreira and M. Sanchis, On C-compact subsets, Houston J. Math., 23, (1997), 65-86.
11. α-compact subsets, Top. and Appl. 77, (1997), 139-160.
12. α-compact subsets, to appear in Czech. J. Math.
13. L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand Reinhold, New York, 1960.
14. J. Ginsburg and V. Saks, Some applications of ultrafilters in topology, Pacific J. Math. 57, (1975), 403-418.
15. E. Hewitt, Rings of real-valued continuous functions, Trans. Amer. Math. Soc. 64, (1948), 45-99.
16. M. Katětov, Characters and types of point sets, Fund. Math. 50, (1961), 369-380.
17. M. Katětov, Products of filters, Comment. Math. Univ. Carolinae 9, (1968), 173-189.
18. P.J. Nyikos and H.C. Reichel, Topologically Orderable Groups, Gen. Topology and Appl. 5, (1975), 195-204.
19. W. Roelcke and S. Dierolf, Uniform Structures on Topological Groups and their Quotients, McGraw-Hill, New York, 1981.
20. D.B. Shakhmatov, A pseudocompact Tychonoff space all countable subsets of which are closed and C*-embedded, Top. and its Appl. 22, (1986), 139-144.
21. p(X) σ-countably compact?, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 94, (1986). No. 1, 70-72. (Russian) English transi. Moscow Univ. Math. Bull. 41, (1986), No. 1, 73-75.
22. L.A. Steen, A direct proof that a linearly ordered space is hereditarily collectionwise normal, Proc. Amer. Math. Soc. 24, (1970), 727-728.
23. M. Sanchis and A. Tamariz-Mascarua, p-pseudocompactness in topological spaces and related topics in topological spaces, Top. and Appl. 98, (1999), 323-343.
24. M. Sanchis and A. Tamariz-Mascarúa, On quasi-p-bounded subsets, Coll. Math. 80, (1999), 175-189.
25. M.G. Tkaěnko, Compactness type properties in topological groups, Czech. Math. J. 113, (1988), 324-341.
26. p(X): Decomposition into a countable unions of bounded subspaces and completeness properties, Topology ant its Applications 22, (1986), 241-253.
27. M. Venkataraman, M. Rajagopalan and T. Soundararajan, Orderable Topological Spaces, Gen. Topology and Appl. 2, (1972), 1-10.
28. J.E. Vaughan, Countably compact and sequentially compact spaces, Handbook of Set Theoretic Topology, Ch. 12, (K. Kunen and J.E. Vaughan, eds.), North Holland, Amsterdam, 1984, 569-602.