Separate and Joint Continuity of Homomorphisms Defined on Topological Groups

نویسندگان

  • Jiling Cao
  • Warren B. Moors
چکیده

In this paper we prove the following theorem. “Let H be a countably Čech–complete topological group, X be a topological space and (G, ·, τ) be a topological group. If f : H ×X → G is a separately continuous mapping with the property that for each x ∈ X, the mapping h 7→ f(h, x) is a group homomorphism, then for each q–point x0 ∈ X the mapping f is jointly continuous at each point of H ×{x0}.” We also present some applications of this result.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\ Vector Spaces

In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {bf5}textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other...

متن کامل

CONTINUITY IN FUNDAMENTAL LOCALLY MULTIPLICATIVE TOPOLOGICAL ALGEBRAS

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

متن کامل

Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups  including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...

متن کامل

Souslin measurable homomorphisms of topological groups

1. In a recent paper [18], A. Kleppner proved that every Haar measurable homomorphism 4 : G ~ H between locally compact groups G, H is continuous. This result also follows from a measure theoretic result by D. H. Fremlin [8], (see also [9, 19]), which provides a technique to prove measurability of uncountable unions of measurable sets. The purpose of this note is to present a different and new ...

متن کامل

Boundedness of linear order-homomorphisms in $L$-topological vector spaces

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015